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SAT II Math I : Solving Equations

Study concepts, example questions & explanations for SAT II Math I

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All SAT II Math I Resources

6 Diagnostic Tests 113 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Single Variable Algebra

Solve for $\displaystyle n$.

$\frac{n}{4}-9=9$ $\displaystyle \frac{n}{4}-9=9$

Possible Answers:

$\displaystyle 0$

$\displaystyle 72$

$\displaystyle 81$

$\displaystyle -18$

$\displaystyle 36$

Correct answer:

$\displaystyle 72$

Explanation:

Add 9 to each side of the equation.

$\frac{n}{4}=18$ $\displaystyle \frac{n}{4}=18$

Multiply each side of the equation by 4.

n=72 $\displaystyle n=72$

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Example Question #1 : Solving Equations

Solve for $\displaystyle m$.

$\frac{2m+5}{3} = 7$ $\displaystyle \frac{2m+5}{3} = 7$

Possible Answers:

m=9 $\displaystyle m=9$

m=6 $\displaystyle m=6$

m=7 $\displaystyle m=7$

m= 8 $\displaystyle m= 8$

Correct answer:

m= 8 $\displaystyle m= 8$

Explanation:

To isolate $\displaystyle m$, we must first eliminate the fraction on the left hand side by multiplying each side by 3.

$\frac{2m+5}{3} *3 = 7 *3$ $\displaystyle \frac{2m+5}{3} *3 = 7 *3$

2m+5=21 $\displaystyle 2m+5=21$

Next, 5 must be subtracted fromm both sides.

$\displaystyle (2m+5)-5=21-5$

2m=16 $\displaystyle 2m=16$

Finally, 2 must be divided out of each side.

$\frac{2m}{2}=\frac{16}{2}$ $\displaystyle \frac{2m}{2}=\frac{16}{2}$

m=8 $\displaystyle m=8$

Thus, this is our answer.

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Example Question #2 : Solving Equations

Solve for $\small y$ $\displaystyle \small y$ in terms of $\displaystyle x$:

$\small \small 8y+3xy-6=2$ $\displaystyle \small \small 8y+3xy-6=2$

Possible Answers:

$\small \frac{-4}{8-3x}$ $\displaystyle \small \frac{-4}{8-3x}$

$\small \frac{8}{8-3x}$ $\displaystyle \small \frac{8}{8-3x}$

$\small \frac{-4}{8+3x}$ $\displaystyle \small \frac{-4}{8+3x}$

$\small \frac{8}{8+3x}$ $\displaystyle \small \frac{8}{8+3x}$

Correct answer:

$\small \frac{8}{8+3x}$ $\displaystyle \small \frac{8}{8+3x}$

Explanation:

$\small \small 8y+3xy-6=2$ $\displaystyle \small \small 8y+3xy-6=2$

To solve this equation in terms of y, we must isolate it. We start by moving those terms, that do not involve y, to the right hand side. Thus, we add 6 to both sides.

$\small 8y+3xy=8$ $\displaystyle \small 8y+3xy=8$

Next, since there are no other terms on the left hand side that do not include y, we must factor a y out of them.

$\small y(8+3x)=8$ $\displaystyle \small y(8+3x)=8$

Now, we can divide to isolate y.

$\small y=\frac{8}{8+3x}$ $\displaystyle \small y=\frac{8}{8+3x}$

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Example Question #3 : Solving Equations

Solve for the unknown variable: $\displaystyle 6-x=6x-6$

Possible Answers:

$\frac{12}{7}$ $\displaystyle \frac{12}{7}$

$\displaystyle -6$

$\frac{7}{12}$ $\displaystyle \frac{7}{12}$

$\frac{1}{6}$ $\displaystyle \frac{1}{6}$

$\displaystyle 1$

Correct answer:

$\frac{12}{7}$ $\displaystyle \frac{12}{7}$

Explanation:

To solve $\displaystyle 6-x=6x-6$, group like terms on one side of the equal sign.

$\displaystyle 6-x+(x)=6x-6+(x)$

6=7x-6 $\displaystyle 6=7x-6$

12=7x $\displaystyle 12=7x$

$x=\frac{12}{7}$ $\displaystyle x=\frac{12}{7}$

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Example Question #11 : Single Variable Algebra

Solve for $\displaystyle x$.

$\displaystyle 19x+34=15$

Possible Answers:

$\displaystyle -3$

$\displaystyle 3$

$\displaystyle 2$

$\displaystyle -1$

$\displaystyle 1$

Correct answer:

$\displaystyle -1$

Explanation:

To isolate the variable in the equation, perform the opposite operation to move all constants on one side of the equation and leaving the variable on the other side of the equation.

$\displaystyle 19x+34=15$

Subtract $\displaystyle 34$ on both sides. Since $\displaystyle 34$ is greater than $\displaystyle 15$ and is negative, our answer is negative. We treat as a normal subtraction.

19x=-19 $\displaystyle 19x=-19$

Divide $\displaystyle 19$ on both sides. When dividing with a negative number, our answer is negative.

x=-1 $\displaystyle x=-1$

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Example Question #4 : Solving Equations

Solve for $\displaystyle x$.

$\displaystyle 13x+45=-72$

Possible Answers:

$\displaystyle 2$

$\displaystyle -9$

$\displaystyle 9$

$\displaystyle 6$

$\displaystyle -2$

Correct answer:

$\displaystyle -9$

Explanation:

To isolate the variable in the equation, perform the opposite operation to move all constants on one side of the equation and leaving the variable on the other side of the equation.

$\displaystyle 13x+45=-72$

Subtract $\displaystyle 45$ on both sides. When adding with another negative number, just treat as an addition problem and then add a negative sign in front.

$\displaystyle 13x=-117$

Divide $\displaystyle 13$ on both sides. When dividing with a negative number, our answer is negative.

x=-9 $\displaystyle x=-9$

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Example Question #1 : Solving Equations

$\frac{x}{14}+34=62$ $\displaystyle \frac{x}{14}+34=62$

Possible Answers:

$\displaystyle 92$

352 $\displaystyle 352$

392 $\displaystyle 392$

312 $\displaystyle 312$

$\displaystyle 2$

Correct answer:

392 $\displaystyle 392$

Explanation:

To isolate the variable in the equation, perform the opposite operation to move all constants on one side of the equation and leaving the variable on the other side of the equation.

$\frac{x}{14}+34=62$ $\displaystyle \frac{x}{14}+34=62$

Subtract $\displaystyle 34$ on both sides.

$\frac{x}{14}=28$ $\displaystyle \frac{x}{14}=28$

Multiply $\displaystyle 14$ on both sides.

x=392 $\displaystyle x=392$

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Example Question #171 : Sat Subject Test In Math I

Solve for $\displaystyle x$.

$\frac{x}{-7}+12=-14$ $\displaystyle \frac{x}{-7}+12=-14$

Possible Answers:

$\displaystyle -182$

182 $\displaystyle 182$

152 $\displaystyle 152$

242 $\displaystyle 242$

$\displaystyle -152$

Correct answer:

182 $\displaystyle 182$

Explanation:

To isolate the variable in the equation, perform the opposite operation to move all constants on one side of the equation and leaving the variable on the other side of the equation.

$\frac{x}{-7}+12=-14$ $\displaystyle \frac{x}{-7}+12=-14$

Subtract $\displaystyle 12$ on both sides. When adding with another negative number, just treat as an addition problem and then add a negative sign in front.

$\frac{x}{-7}=-26$ $\displaystyle \frac{x}{-7}=-26$

Multiply $\displaystyle -7$ on both sides. When multiplying with another negative number, our answer is positive.

x=162 $\displaystyle x=162$

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Example Question #1 : Solving Equations

Solve for $\displaystyle x$.

$\displaystyle 15x-45=60$

Possible Answers:

$\displaystyle 9$

$\displaystyle 3$

$\displaystyle 1$

$\displaystyle 7$

$\displaystyle 5$

Correct answer:

$\displaystyle 7$

Explanation:

To isolate the variable in the equation, perform the opposite operation to move all constants on one side of the equation and leaving the variable on the other side of the equation.

$\displaystyle 15x-45=60$

Add $\displaystyle 45$ to both sides.

15x=105 $\displaystyle 15x=105$

Divide $\displaystyle 15$ on both sides.

x=7 $\displaystyle x=7$

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Example Question #3 : Solving Equations

$\displaystyle 11x-72=-215$

Possible Answers:

$\displaystyle -23$

$\displaystyle -11$

$\displaystyle 23$

$\displaystyle 13$

$\displaystyle -13$

Correct answer:

$\displaystyle -13$

Explanation:

To isolate the variable in the equation, perform the opposite operation to move all constants on one side of the equation and leaving the variable on the other side of the equation.

$\displaystyle 11x-72=-215$

Add $\displaystyle 72$ on both sides. Since 215 $\displaystyle 215$ is greater than $\displaystyle 72$ and is negative, our answer is negative. We treat as a normal subtraction.

$\displaystyle 11x=-143$

Divide $\displaystyle 11$ on both sides. When dividing with a negative number, our answer is negative.

x=-13 $\displaystyle x=-13$

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SAT II Math I : Solving Equations

Study concepts, example questions & explanations for SAT II Math I

All SAT II Math I Resources

Example Questions

Example Question #1 : Single Variable Algebra

Example Question #1 : Solving Equations

Example Question #2 : Solving Equations

Example Question #3 : Solving Equations

Example Question #11 : Single Variable Algebra

Example Question #4 : Solving Equations

Example Question #1 : Solving Equations

Example Question #171 : Sat Subject Test In Math I

Example Question #1 : Solving Equations

Example Question #3 : Solving Equations

All SAT II Math I Resources

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