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ISEE Middle Level Math : How to find the solution to an equation

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

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All ISEE Middle Level Math Resources

6 Diagnostic Tests 303 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #541 : Algebraic Concepts

Solve the following equations when y=5 $\displaystyle y=5$ .

y=2x-3 $\displaystyle y=2x-3$

Possible Answers:

$\displaystyle 5$

$\displaystyle 2$

$\displaystyle 3$

$\displaystyle -3$

$\displaystyle 4$

Correct answer:

$\displaystyle 4$

Explanation:

The first step to solve this equation is to plug in your know variable $\displaystyle y$ with the value given, $\displaystyle 5$ .

Now you have an expression that reads 5=2x-3 $\displaystyle 5=2x-3$ and we now solve for $\displaystyle x$ .

First you must move the constant $\displaystyle -3$ by adding $\displaystyle 3$ to both sides resulting in,

8=2x $\displaystyle 8=2x$ .

The last step is to divide both sides by $\displaystyle 2$ resulting in,

x=4 $\displaystyle x=4$ .

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Example Question #542 : Algebraic Concepts

Solve for $\displaystyle y$ when x=6 $\displaystyle x=6$ :

$y=\frac{x}{2}+7$ $\displaystyle y=\frac{x}{2}+7$

Possible Answers:

$\displaystyle 6$

$\displaystyle 10$

$\displaystyle 2$

$\displaystyle 13$

$\displaystyle 7$

Correct answer:

$\displaystyle 10$

Explanation:

The first is to plug in the $\displaystyle x$ value given in the problem leaving us with,

$y=\frac{6}{2}+7$ $\displaystyle y=\frac{6}{2}+7$ .

The next step is to complete the division which is

$6\div2=3$ $\displaystyle 6\div2=3$ .

Then you add the constant and that gives you an answer of,

3+7=10 $\displaystyle 3+7=10$ .

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Example Question #543 : Algebraic Concepts

Solve for $\displaystyle x$ :

$\displaystyle 9x + 2.3 =-10.3$

Possible Answers:

$\displaystyle x = -1.4$

x = 1.4 $\displaystyle x = 1.4$

$\displaystyle x = 12.6$

$\displaystyle x = -12.6$

Correct answer:

$\displaystyle x = -1.4$

Explanation:

This is a two-step equation. The first step is to isolate the variable. Subtract 2.3 from both sides of the equation:

$\displaystyle 9x +2.3 -2.3 = -10.3 - 2.3$

$\displaystyle 9x = -12.6$

Divide both sides of the equation by the coefficient which is 9:

$\displaystyle x = -1.4$

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Example Question #544 : Algebraic Concepts

$\frac{1}{2}x + 3 = 5$ $\displaystyle \frac{1}{2}x + 3 = 5$

Possible Answers:

x = 0 $\displaystyle x = 0$

x = 5 $\displaystyle x = 5$

x = 4 $\displaystyle x = 4$

x = 8 $\displaystyle x = 8$

Correct answer:

x = 4 $\displaystyle x = 4$

Explanation:

To isolate the variable, subtract 3 from both sides of the equation:

$\frac{1}{2}x + 3-3 = 5-3$ $\displaystyle \frac{1}{2}x + 3-3 = 5-3$

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

Multiply both sides of the equation by the reciprocal of $\frac{1}{2}$ $\displaystyle \frac{1}{2}$ which is $\frac{2}{1}$ $\displaystyle \frac{2}{1}$

$\frac{1}{2}\times(\frac2{}{1}) = 2 \times \frac{2}{1}$ $\displaystyle \frac{1}{2}\times(\frac2{}{1}) = 2 \times \frac{2}{1}$

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

x = 4 $\displaystyle x = 4$

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Example Question #341 : How To Find The Solution To An Equation

Find the solution to the following equation when t=6 $\displaystyle t=6$ .

$\displaystyle y=2t^2-6t-36$

Possible Answers:

$\displaystyle 36$

$\displaystyle 72$

$\displaystyle 0$

$\displaystyle 12$

Correct answer:

$\displaystyle 0$

Explanation:

Find the solution to the following equation when t=6 $\displaystyle t=6$ .

$\displaystyle y=2t^2-6t-36$

To solve this equation, we should plug in 6 wherever there is a t, and simplify.

$\displaystyle y=2(6)^2-6(6)-36=72-36-36=0$

So, our answer when t=6 is 0.

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Example Question #552 : Algebraic Concepts

Find b when f=6 $\displaystyle f=6$ , and c=4 $\displaystyle c=4$

$\displaystyle b=3f^3-4c^4$ .

Possible Answers:

b=16 $\displaystyle b=16$

b=487 $\displaystyle b=487$

b=-376 $\displaystyle b=-376$

b=376 $\displaystyle b=376$

Correct answer:

b=-376 $\displaystyle b=-376$

Explanation:

Find b when f=6 $\displaystyle f=6$ , and c=4 $\displaystyle c=4$

$\displaystyle b=3f^3-4c^4$

To find b, we want to plug in f and c and simplify:

$\displaystyle b=3(6)^3-4(4)^4=3(216)-1024$

$\displaystyle 3(216)-1024=648-1024=-376$

So our answer is

b=-376 $\displaystyle b=-376$

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Example Question #341 : How To Find The Solution To An Equation

Solve: $11^{2}-4^{3}$ $\displaystyle 11^{2}-4^{3}$

Possible Answers:

$\displaystyle 57$

121 $\displaystyle 121$

185 $\displaystyle 185$

$\displaystyle 64$

Correct answer:

$\displaystyle 57$

Explanation:

To solve, first solve the exponents:

$11^{2}=121$ $\displaystyle 11^{2}=121$

$4^{3}=64$ $\displaystyle 4^{3}=64$

Then solve the equation: $\displaystyle 121-64=57$

Answer: $\displaystyle 57$

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Example Question #342 : How To Find The Solution To An Equation

Solve: $5^{3}*2^{3}$ $\displaystyle 5^{3}*2^{3}$

Possible Answers:

100 $\displaystyle 100$

117 $\displaystyle 117$

1000 $\displaystyle 1000$

131 $\displaystyle 131$

Correct answer:

1000 $\displaystyle 1000$

Explanation:

To solve, first solve the exponents:

$5^{3}=125$ $\displaystyle 5^{3}=125$

$2^{3}=8$ $\displaystyle 2^{3}=8$

Then solve the equation: $\displaystyle 125*8=1000$

Answer: 1000 $\displaystyle 1000$

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Example Question #2671 : Isee Middle Level (Grades 7 8) Mathematics Achievement

Solve for $\displaystyle t$ :

13t=169 $\displaystyle 13t=169$

Possible Answers:

$\displaystyle 14$

182 $\displaystyle 182$

156 $\displaystyle 156$

$\displaystyle 13$

Correct answer:

$\displaystyle 13$

Explanation:

To solve, divide each side by 13:

$13t\div 13=169\div 13$ $\displaystyle 13t\div 13=169\div 13$

t=13 $\displaystyle t=13$

Answer: $\displaystyle 13$

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Example Question #2672 : Isee Middle Level (Grades 7 8) Mathematics Achievement

Solve for $\displaystyle m$ :

44m=308 $\displaystyle 44m=308$

Possible Answers:

$\displaystyle 6$

$\displaystyle 8$

$\displaystyle 7$

$\displaystyle 9$

Correct answer:

$\displaystyle 7$

Explanation:

To solve, divide each side by $\displaystyle 44$ :

$44m\div 44=308\div 44$ $\displaystyle 44m\div 44=308\div 44$

m=7 $\displaystyle m=7$

Answer: $\displaystyle 7$

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All ISEE Middle Level Math Resources

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ISEE Middle Level Math : How to find the solution to an equation

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

All ISEE Middle Level Math Resources

Example Questions

Example Question #541 : Algebraic Concepts

Example Question #542 : Algebraic Concepts

Example Question #543 : Algebraic Concepts

Example Question #544 : Algebraic Concepts

Example Question #341 : How To Find The Solution To An Equation

Example Question #552 : Algebraic Concepts

Example Question #341 : How To Find The Solution To An Equation

Example Question #342 : How To Find The Solution To An Equation

Example Question #2671 : Isee Middle Level (Grades 7 8) Mathematics Achievement

Example Question #2672 : Isee Middle Level (Grades 7 8) Mathematics Achievement

All ISEE Middle Level Math Resources

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