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Algebra 1 : How to find the solution to an inequality with addition

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Example Question #43 : Equations / Inequalities

Solve this inequality:

5x -2 < 8 - x

Possible Answers:

$x < \frac{5}{2}$

$x < \frac{7}{3}$

$x > \frac{5}{3}$

$x < \frac{3}{2}$

$x < \frac{5}{3}$

Correct answer:

$x < \frac{5}{3}$

Explanation:

First, add to both sides:

5x -2 +x < 8 - x + x , or

6x -2 < 8 .

Then, add 2 to both sides:

6x - 2 + 2 < 8 + 2 , or

6x < 10

Finally, divide both sides by 6 to get the answer:

$x < \frac{10}{6}$

which simplifies to:

$x < \frac{5}{3}$

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Example Question #2172 : Algebra 1

Solve for :

x+3>2x-9

Possible Answers:

x>12

x>6

None of the other answers

x<6

x<12

Correct answer:

x<12

Explanation:

To solve the inequality, simply move the 's to one side and the integers to the other (i.e. subtract from both sides and add 9 to both sides). This gives you x<12 .

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Example Question #1 : How To Find The Solution To An Inequality With Addition

Solve for :

x+5>3x-3

Possible Answers:

x<4

x<2

x>1

x<1

x>4

Correct answer:

x<4

Explanation:

Subtracting and adding 3 to both sides of the equation of x+5>3x-3 will give you 8>2x . Divide both sides by 2 to get x<4 .

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

Which value of is in the solution set of the inequality 2x+2>-x+17 ?

Possible Answers:

Correct answer:

Explanation:

Add and subtract 2 from both sides of 2x+2>-x+17 to get 3x>15 . Then, divide both sides by 3 to get a solution of x>5 . The only answer choice that is greater than 5 is 6.

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

Find the solution set for :

$3.2 \geq -x + 0.6 > -5.1$

Possible Answers:

[-5.7, -2.6)

(-5.7, -2.6]

(-5.7, 2.6]

[2.6, 5.7)

[-2.6, 5.7)

Correct answer:

[-2.6, 5.7)

Explanation:

$3.2 \geq -x + 0.6 > -5.1$

$3.2- 0.6 \geq -x + 0.6 - 0.6 > -5.1 - 0.6$

$2.6 \geq -x > -5.7$

$2.6 \cdot (-1 )\leq -x \cdot (-1 )< -5.7 \cdot (-1 )$

Note the switch in inequality symbols when the numbers are multiplied by a negative number.

$-2.6 \leq x < 5.7$

or, in interval notation, [-2.6, 5.7)

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Example Question #51 : Systems Of Inequalities

Solve the inequality:

3+x-5<2

Possible Answers:

x<-6

x<0

x<10

No solution

x<4

Correct answer:

x<4

Explanation:

Combine like-terms on the left side of the inequality: x-2<2 . Next, isolate the variable: $x-2 \boldsymbol{+2} <2 \boldsymbol{+2}$ .

Therefore the answer is x<4 .

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Example Question #52 : Systems Of Inequalities

Solve:

$\small x+2\geq 7$

Possible Answers:

None of the other answers are correct.

$\small x\geq 5$

$\small x> 5$

$\small x\leq 9$

$\small x< 9$

Correct answer:

$\small x\geq 5$

Explanation:

Subtract 2 from each side:

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

$\small x\geq 5$

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Example Question #53 : Systems Of Inequalities

Solve for :

2x-4 >7

Possible Answers:

x>3.5

x>11

x>1.5

x>22

x>5.5

Correct answer:

x>5.5

Explanation:

This inequality can be solved just like an equation.

Add 4 to both sides:

2x > 11

Then divide by 2:

x > 11/2 = 5.5

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Example Question #7 : How To Find The Solution To An Inequality With Addition

Solve the inequality:

$\small 15x - 4 \le 2x + 8 +x$

Possible Answers:

$\small x \le1$

$\small x \le \frac{4}{5}$

$\small x \le \frac{6}{7}$

$\small x \le \frac{11}{14}$

$\small x \le 0$

Correct answer:

$\small x \le1$

Explanation:

First, combine like terms on a single side of the inequality. On the right side of the inequality, combine the terms to obtain $\small 15x - 4 \le 3x +8$ .

Next, we want to get all the variables on the left side of the inequality and all of the constants on the right side of the inequality. Add 4 to both sides and subtract from both sides to get $\small 12x \le 12$ .

Finally, to isolate the variable, divide both sides by 12 to produce the final answer, $\small x \le1$ .

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Example Question #54 : Systems Of Inequalities

Solve: x-3<50

Possible Answers:

$x\leq 53$

x> 53

x<47

$x\leq 47$

x<53

Correct answer:

x<53

Explanation:

To solve x-3<50 , isolate the variable by adding three on both sides.

x-3+(3)<50+(3)

The correct answer is: x<53

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Algebra 1 : How to find the solution to an inequality with addition

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #43 : Equations / Inequalities

Example Question #2172 : Algebra 1

Example Question #1 : How To Find The Solution To An Inequality With Addition

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

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

Example Question #51 : Systems Of Inequalities

Example Question #52 : Systems Of Inequalities

Example Question #53 : Systems Of Inequalities

Example Question #7 : How To Find The Solution To An Inequality With Addition

Example Question #54 : Systems Of Inequalities

All Algebra 1 Resources

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