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SSAT Middle Level Math : Equations

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Example Questions

Example Question #21 : Ssat Middle Level Quantitative (Math)

Solve for $\displaystyle x$:

$\displaystyle -5x = -70$

Possible Answers:

x = 350 $\displaystyle x = 350$

x = -75 $\displaystyle x = -75$

x = 14 $\displaystyle x = 14$

x = -65 $\displaystyle x = -65$

x = -14 $\displaystyle x = -14$

Correct answer:

x = 14 $\displaystyle x = 14$

Explanation:

Divide both sides by $\displaystyle -5$:

$\displaystyle -5x = -70$

$-5x \div (-5) = -70 \div (-5)$ $\displaystyle -5x \div (-5) = -70 \div (-5)$

$x = -70 \div (-5) = + (70\div 5) = 14$ $\displaystyle x = -70 \div (-5) = + (70\div 5) = 14$

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Example Question #21 : How To Find The Solution To An Equation

Solve for $\displaystyle x$:

$\displaystyle x - 28 = 82$

Possible Answers:

x = 54 $\displaystyle x = 54$

x = 44 $\displaystyle x = 44$

x = 64 $\displaystyle x = 64$

x = 100 $\displaystyle x = 100$

x = 110 $\displaystyle x = 110$

Correct answer:

x = 110 $\displaystyle x = 110$

Explanation:

Add 28 to both sides:

$\displaystyle x - 28 = 82$

$\displaystyle x - 28 + 28 = 82 + 28$

x = 110 $\displaystyle x = 110$

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Example Question #21 : Equations

Solve for $\displaystyle x$:

$\displaystyle 3x - 9= 30$

Possible Answers:

x = 13 $\displaystyle x = 13$

x = 17 $\displaystyle x = 17$

x = 9 $\displaystyle x = 9$

x= 11 $\displaystyle x= 11$

x = 7 $\displaystyle x = 7$

Correct answer:

x = 13 $\displaystyle x = 13$

Explanation:

$\displaystyle 3x - 9= 30$

$\displaystyle 3x - 9 + 9= 30+ 9$

3x = 39 $\displaystyle 3x = 39$

$3x \div 3 = 39 \div 3$ $\displaystyle 3x \div 3 = 39 \div 3$

x = 13 $\displaystyle x = 13$

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Example Question #22 : Equations

Solve for $\displaystyle x$:

$\displaystyle 3x + 9= 30$

Possible Answers:

x = 11 $\displaystyle x = 11$

x = 5 $\displaystyle x = 5$

x = 12 $\displaystyle x = 12$

x = 7 $\displaystyle x = 7$

x = 8 $\displaystyle x = 8$

Correct answer:

x = 7 $\displaystyle x = 7$

Explanation:

$\displaystyle 3x + 9= 30$

$\displaystyle 3x + 9 - 9= 30- 9$

3x = 21 $\displaystyle 3x = 21$

$3x \div 3 = 21 \div 3$ $\displaystyle 3x \div 3 = 21 \div 3$

x = 7 $\displaystyle x = 7$

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Example Question #24 : How To Find The Solution To An Equation

Call the three angles of a triangle $\angle 1, \angle 2, \angle 3$ $\displaystyle \angle 1, \angle 2, \angle 3$.

The measure of $\angle2$ $\displaystyle \angle2$ is twenty degrees greater than that of $\angle 1$ $\displaystyle \angle 1$; the measure of $\angle 3$ $\displaystyle \angle 3$ is thirty degrees less than twice that of $\angle 1$ $\displaystyle \angle 1$. If $\displaystyle x$ is the measure of $\angle 1$ $\displaystyle \angle 1$, then which of the following equations would we need to solve in order to calculate the measures of the angles?

Possible Answers:

$\displaystyle x + (x-20) + 2(x-30) = 180$

$\displaystyle x + (x+20) + (2x-30) = 360$

$\displaystyle x + (x-20) + 2(x-30) = 360$

$\displaystyle x + (x+20) + (2x-30) = 180$

$\displaystyle x + (x+20) = (2x+30)$

Correct answer:

$\displaystyle x + (x+20) + (2x-30) = 180$

Explanation:

The measure of $\angle2$ $\displaystyle \angle2$ is twenty degrees greater than the measure $\displaystyle x$ of $\angle 1$ $\displaystyle \angle 1$, so its measure is 20 added to that of $\angle 1$ $\displaystyle \angle 1$ - that is, x + 2 0 $\displaystyle x + 2 0$.

The measure of $\angle 3$ $\displaystyle \angle 3$ is thirty degrees less than twice that of $\angle 1$ $\displaystyle \angle 1$. Twice the measure of $\angle 1$ $\displaystyle \angle 1$ is $\displaystyle 2x$, and thirty degrees less than this is 30 subtracted from $\displaystyle 2x$ - that is, 2x-30 $\displaystyle 2x-30$.

The sum of the measures of the three angles of a triangle is 180, so, to solve for $\displaystyle x$ - thereby allowing us to calulate all three angle measures - we add these three expressions and set the sum equal to 180. This yields the equation:

$\displaystyle x + (x+20) + (2x-30) = 180$

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Example Question #3 : How To Find The Measure Of An Angle

Call the three angles of a triangle $\angle 1, \angle 2, \angle 3$ $\displaystyle \angle 1, \angle 2, \angle 3$.

The measure of $\angle2$ $\displaystyle \angle2$ is forty degrees less than that of $\angle 1$ $\displaystyle \angle 1$; the measure of $\angle 3$ $\displaystyle \angle 3$ is ten degrees less than twice that of $\angle 1$ $\displaystyle \angle 1$. If $\displaystyle x$ is the measure of $\angle 1$ $\displaystyle \angle 1$, then which of the following equations would we need to solve in order to calculate the measures of the angles?

Possible Answers:

$\displaystyle x + (x-40) + 2 (x - 10) = 360$

$\displaystyle x + (x-40) = (2x - 10)$

$\displaystyle x + (x-40) + (2x - 10) = 360$

$\displaystyle x + (x-40) + (2x - 10) = 180$

$\displaystyle x + (x-40) + 2 (x - 10) = 180$

Correct answer:

$\displaystyle x + (x-40) + (2x - 10) = 180$

Explanation:

The measure of $\angle2$ $\displaystyle \angle2$ is forty degrees less than the measure $\displaystyle x$ of $\angle 1$ $\displaystyle \angle 1$, so its measure is 40 subtracted from that of $\angle 1$ $\displaystyle \angle 1$ - that is, x -40 $\displaystyle x -40$.

The measure of $\angle 3$ $\displaystyle \angle 3$ is ten degrees less than twice that of $\angle 1$ $\displaystyle \angle 1$. Twice the measure of $\angle 1$ $\displaystyle \angle 1$ is $\displaystyle 2x$, and ten degrees less than this is 10 subtracted from $\displaystyle 2x$ - that is, 2x-10 $\displaystyle 2x-10$.

$\displaystyle x + (x-40) + (2x - 10) = 180$

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Example Question #25 : How To Find The Solution To An Equation

Solve for $\displaystyle x$:

$\displaystyle -5 (x-12) = -35$

Possible Answers:

x=-7 $\displaystyle x=-7$

x=-18 $\displaystyle x=-18$

x=-5 $\displaystyle x=-5$

x=42 $\displaystyle x=42$

x=19 $\displaystyle x=19$

Correct answer:

x=19 $\displaystyle x=19$

Explanation:

$\displaystyle -5 (x-12) = -35$

$-5 \cdot x- \left (-5 \right ) \cdot 12 = -35$ $\displaystyle -5 \cdot x- \left (-5 \right ) \cdot 12 = -35$

$-5x- \left (-60 \right ) = -35$ $\displaystyle -5x- \left (-60 \right ) = -35$

$\displaystyle -5x+60= -35$

$\displaystyle -5x+60 -60= -35-60$

$\displaystyle -5x= -95$

$-5x \div (-5)= -95\div (-5)$ $\displaystyle -5x \div (-5)= -95\div (-5)$

x=19 $\displaystyle x=19$

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Example Question #23 : Equations

Solve for $\displaystyle x$:

$\displaystyle 5x + 15 = x + 84$

Possible Answers:

$x=16\frac{1}{2}$ $\displaystyle x=16\frac{1}{2}$

$x = 17\frac{1}{4}$ $\displaystyle x = 17\frac{1}{4}$

$x=24\frac{3}{4}$ $\displaystyle x=24\frac{3}{4}$

$x= 13\frac{4}{5}$ $\displaystyle x= 13\frac{4}{5}$

$x=11\frac{1}{2}$ $\displaystyle x=11\frac{1}{2}$

Correct answer:

$x = 17\frac{1}{4}$ $\displaystyle x = 17\frac{1}{4}$

Explanation:

$\displaystyle 5x + 15 = x + 84$

$\displaystyle 5x -x+ 15 = x-x + 84$

$\displaystyle 4x+ 15 = 84$

$\displaystyle 4x+ 15-15 = 84-15$

4x = 69 $\displaystyle 4x = 69$

$4x \div 4= 69\div 4$ $\displaystyle 4x \div 4= 69\div 4$

$x = 17\frac{1}{4}$ $\displaystyle x = 17\frac{1}{4}$

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Example Question #27 : How To Find The Solution To An Equation

Solve for $\displaystyle x$:

$\displaystyle 3x -21=66$

Possible Answers:

x=69 $\displaystyle x=69$

x=15 $\displaystyle x=15$

x=29 $\displaystyle x=29$

x=207 $\displaystyle x=207$

x=45 $\displaystyle x=45$

Correct answer:

x=29 $\displaystyle x=29$

Explanation:

$\displaystyle 3x -21=66$

$\displaystyle 3x -21+ 21=66+ 21$

3x =87 $\displaystyle 3x =87$

$3x\div 3=87\div 3$ $\displaystyle 3x\div 3=87\div 3$

x=29 $\displaystyle x=29$

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Example Question #23 : Ssat Middle Level Quantitative (Math)

Solve for $\displaystyle x$:

$\displaystyle 4x - 15 = x + 84$

Possible Answers:

$x= 24\frac{3}{4}$ $\displaystyle x= 24\frac{3}{4}$

x=33 $\displaystyle x=33$

x= 23 $\displaystyle x= 23$

$x = 17 \frac{1}{4}$ $\displaystyle x = 17 \frac{1}{4}$

$x = 13 \frac{4}{5}$ $\displaystyle x = 13 \frac{4}{5}$

Correct answer:

x=33 $\displaystyle x=33$

Explanation:

$\displaystyle 4x - 15 = x + 84$

$\displaystyle 4x-x - 15 = x -x+ 84$

$\displaystyle 3x - 15 = 84$

$\displaystyle 3x - 15 +15= 84+15$

3x = 99 $\displaystyle 3x = 99$

$3x \div 3 = 99\div 3$ $\displaystyle 3x \div 3 = 99\div 3$

x=33 $\displaystyle x=33$

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SSAT Middle Level Math : Equations

Study concepts, example questions & explanations for SSAT Middle Level Math

All SSAT Middle Level Math Resources

Example Questions

Example Question #21 : Ssat Middle Level Quantitative (Math)

Example Question #21 : How To Find The Solution To An Equation

Example Question #21 : Equations

Example Question #22 : Equations

Example Question #24 : How To Find The Solution To An Equation

Example Question #3 : How To Find The Measure Of An Angle

Example Question #25 : How To Find The Solution To An Equation

Example Question #23 : Equations

Example Question #27 : How To Find The Solution To An Equation

Example Question #23 : Ssat Middle Level Quantitative (Math)

All SSAT Middle Level Math Resources

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