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SAT Math : SAT Mathematics

Study concepts, example questions & explanations for SAT Math

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Example Questions

Example Question #5 : How To Find The Solution To An Inequality With Addition

Solve for .

4x+7<5x+13

Possible Answers:

x>-6

$x\geq-6$

x=-6

$x\leq-6$

x<-6

Correct answer:

x>-6

Explanation:

We want to isolate the variable on one side and numbers on another side. Treat like a normal equation.

4x+7<5x+13 Subtract 4x,13 on both sides.

x<-6

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Example Question #6 : How To Find The Solution To An Inequality With Addition

Solve for .

$\left | x+5\right |<8$

Possible Answers:

x=3, x=-13

x>3, x<-13

x>3

-13<x<3

x<-13

Correct answer:

-13<x<3

Explanation:

We want to isolate the variable on one side and numbers on another side. Treat like a normal equation.

$\left | x+5\right |<8$ We need to set-up two equations since its absolute value.

x+5<8 Subtract on both sides. x<3

-(x+5)<8 Divide on both sides which flips the sign.

x+5>-8 Subtract on both sides. x>-13

Since we have the 's being either greater than or less than the values, we can combine them to get -13<x<3 .

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Example Question #23 : Inequalities

Solve for .

$\left | x+7\right |\leq3x+13$

Possible Answers:

$-3\leq x$

$3\leq x\leq 5$

$x\leq -3, x\leq -5$

$-5\leq x\leq -3$

$-5\leq x$

Correct answer:

$-3\leq x$

Explanation:

We want to isolate the variable on one side and numbers on another side. Treat like a normal equation.

$\left | x+7\right |\leq3x+13$ We need to set-up two equations since it's absolute value.

$x+7\leq 3x+13$ Subtract x, 7 on both sides.

$-6\leq 2x$ Divide on both sides.

$-3\leq x$

$-(x+7)\leq 3x+13$ Distribute the negative sign to each term in the parenthesis.

$-x-7\leq3x+13$ Add and subtract on both sides.

$-20\leq4x$ Divide on both sides.

$-5\leq x$ We must check each answer. Let's try .

$\left | 0+7\right |<3(0)+13$ 7<13 This is true therefore $-3\leq x$ is a correct answer. Let's next try .

$\left | -4+7\right |<3(-4)+13$ 3<1 This is not true therefore $-5\leq x$ is not correct.

Final answer is just $-3\leq x$ .

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Example Question #6 : How To Find The Solution To An Inequality With Addition

If $x+1< 4$ and $y-2<-1$ , then which of the following could be the value of x+y ?

Possible Answers:

Correct answer:

Explanation:

To solve this problem, add the two equations together:

$x+1<4$

$y-2<-1$

$x+1+y-2<4-1$

$x+y-1<3$

$x+y<4$

The only answer choice that satisfies this equation is 0, because 0 is less than 4.

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Example Question #25 : Inequalities

Solve for :

4x+5<49

Possible Answers:

x=11

x<11

x>11

$x\leq11$

Correct answer:

x<11

Explanation:

We want to isolate the variable on one side and numbers on another side. Treat like a normal equation.

4x+5<49 Subtract on both sides.

4x<44 Divide on both sides.

x<11

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Example Question #26 : Inequalities

Solve for :

$\left | x+5\right |<2x+16$

Possible Answers:

x>-11

x>-7, x<-11

x>-7

-11<x<-7

Correct answer:

x>-7

Explanation:

We want to isolate the variable on one side and numbers on another side. Treat like a normal equation.

$\left | x+5\right |<2x+16$ We need to set-up two equations since it's absolute value.

x+5<2x+16 Subtract x, 16 on both sides.

-11<x

-(x+5)<2x+16 Distribute the negative sign to each term in the parenthesis.

-x-5<2x+16 Add and subtract on both sides.

-21<3x Divide on both sides.

-7<x We must check each answer. Let's try .

$\left | 0+5\right |<2(0)+16$ 5<16 This is true therefore -7<x is a correct answer. Let's next try .

$\left | -8+5\right |<2(-8)+16$ 3<0 This is not true therefore -11<x is not correct.

Final answer is just -7<x .

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Example Question #2 : How To Find The Solution To An Inequality With Multiplication

If –1 < n < 1, all of the following could be true EXCEPT:

Possible Answers:

n² < 2n

(n-1)² > n

n² < n

|n² - 1| > 1

16n² - 1 = 0

Correct answer:

|n² - 1| > 1

Explanation:

N_part_1

N_part_2

N_part_3

N_part_4

N_part_5

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Example Question #3 : How To Find The Solution To An Inequality With Multiplication

(√(8) / -x ) < 2. Which of the following values could be x?

Possible Answers:

All of the answers choices are valid.

-1

-3

-2

-4

Correct answer:

-1

Explanation:

The equation simplifies to x > -1.41. -1 is the answer.

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Example Question #4 : How To Find The Solution To An Inequality With Multiplication

Solve for x

$\small 3x+7 \geq -2x+4$

Possible Answers:

$\small x \geq -\frac{3}{5}$

$\small x \leq -\frac{3}{5}$

$\small x \geq \frac{3}{5}$

$\small x \leq \frac{3}{5}$

Correct answer:

$\small x \geq -\frac{3}{5}$

Explanation:

$\small 3x+7 \geq -2x+4$

$\small 3x \geq -2x-3$

$\small 5x \geq -3$

$\small x\geq -\frac{3}{5}$

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Example Question #5 : How To Find The Solution To An Inequality With Multiplication

We have x^2-4<0 , find the solution set for this inequality.

Possible Answers:

x=0

-2<x<2

x>-2

x<2

x>2, x<-2

Correct answer:

-2<x<2

Explanation:

$x^2-4<0 \Rightarrow x^2<4 \Rightarrow -2<x<2$

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SAT Math : SAT Mathematics

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #5 : How To Find The Solution To An Inequality With Addition

Example Question #6 : How To Find The Solution To An Inequality With Addition

Example Question #23 : Inequalities

Example Question #6 : How To Find The Solution To An Inequality With Addition

Example Question #25 : Inequalities

Example Question #26 : Inequalities

Example Question #2 : How To Find The Solution To An Inequality With Multiplication

Example Question #3 : How To Find The Solution To An Inequality With Multiplication

Example Question #4 : How To Find The Solution To An Inequality With Multiplication

Example Question #5 : How To Find The Solution To An Inequality With Multiplication

All SAT Math Resources

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