1-2 Solving Linear Equations - Weebly

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enVision™ Algebra 1 • Teaching Resources

1-2 Solving Linear Equations

Solve each equation.

1. 2m − 7 = 11 2. −3d + 13 = 43 3. 41 8

p

4. −3 = −3(2t − 4) 5.

2( 6)

48 2

r

6. 8(n + 7) = 24

7. x − 2(x + 10) = 14 8. −25 = 5(3q − 10) − 5q

For Items 9–11, write and solve a linear equation to match each situation.

9. The sum of three consecutive integers is 60. What are the three integers?

10. Olivia ate at the same restaurant four times. Each visit she ordered a salad and left a $2.50 tip. She spent a total of $64. Find the cost c of each salad.

11. A student needs 30 liters of a solution that is 12% acid for a lab, but he only has a solution that is 10% and a solution that is 15%. How many liters of the 10% solution and the 15% solutions should he mix to get what he needs?

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1-3 Additional Practice Solving Equations with a Variable on Both Sides

Identify whether no, one, or infinitely many solutions exist for each equation. If a solution exists, determine the value.

1. 4y − 7 + 2y = −3(y − 1) −1

3. −8x − (3x + 6) = 4 – x

5. 2(4t + 1) = 6t + 5 +2t - 3

7. −6(−p + 8) = −6p + 12

2. −(5a + 6) = 2(3a + 8)

4. 14 + 3n = 8n − 3(n − 4)

6. 31 + m

32 = m

32 −

32

8. 21 r + 6 = 3 − 2r

Solve each problem.

9. A movie club charges a one-time membership fee of $25. It allows members to purchase movies for $7 each. Another club does not charge a membership fee and sells movies for $12 each. How many movies must a member purchase for the total cost of the two clubs to be equal?

10. How many pounds of cashews that cost $14 per pound must be mixed with 5 pounds of peanuts that cost $6.50 per pound to make mixed nuts that cost $10.25 per pound?

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1-4 Additional Practice Literal Equations and Formulas

Rewrite each equation to solve for m.

1. m + 3n = 7

3. 2m = −6n − 5

2. 4n − 6m = −2

4. 10m + 6n = 12

Rewrite each equation to solve for x.

5. d = f + fx 6. −3(x + n) = x 7. m =

p

nx

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1-5 Additional Practice Solving Inequalities in One Variable

Solve each inequality. Then graph the solution.

1. 2y ≤ −3

3. 3(v − 4) ≥ 5v − 24

2. −3(m − 4) < 6

4. −6t − 3 < −2t − 19

Solve each inequality.

5. 2(k + 4) − 3k ≤ 14

7. −53 > −3(3z + 3) + 3z

9. 3(4c − 5) − 2c > 0

6. 22 ≥ 5(2y + 3) − 3y

8. 9 − 2x < 7 + 2(x − 3)

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1-6 Compound Inequalities

1.

Write a compound inequality that represents each phrase. Graph the solution.

2. all real numbers that are less than −8 or greater than or equal to 3

Solve each compound inequality. Graph your solution.

3. 5 < k − 1 < 9

5. 5 − m < 4 or 7m > 35

4. −2 > y + 3 ≥ −10

6. 3 > 4

11 k ≥ −3

Write a compound inequality that each graph could represent.

7.

8.

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1-2 Solving Linear Equations - Weebly