Chapter 1 Study Guide Alg 1

Solve the equation. Check your solution. 4 + y = 9.5

• y = 5.5

• y = 4.5

• y = 6.5

• y = 3.5

Answer explanation

To solve for y in the equation 4 + y = 9.5, subtract 4 from both sides: y = 9.5 - 4, which gives y = 5.5. Checking: 4 + 5.5 = 9.5, confirms the solution. Thus, the correct answer is y = 5.5.

Tags

CCSS.6.EE.B.7

• x = 32

• x = -32

• x = 8

• x = -8

Answer explanation

To solve \( \frac{x}{-4} = -8 \), multiply both sides by -4: \( x = -8 \times -4 = 32 \). Checking: \( \frac{32}{-4} = -8 \) confirms the solution. Thus, the correct answer is \( x = 32 \).

Tags

CCSS.6.EE.B.7

Answer explanation

To solve for z, add \frac{2}{3} to both sides: z = \frac{1}{3} + \frac{2}{3} = 1. Thus, the correct answer is z = 1.

Tags

CCSS.6.EE.B.7

Solve the equation. Check your solution. r - | -4 | = 11

• r = 15

• r = 7

• r = -15

• r = 11

Answer explanation

To solve r - | -4 | = 11, first calculate | -4 | = 4. Then, r - 4 = 11. Adding 4 to both sides gives r = 15. Checking: 15 - 4 = 11, which is correct. Thus, the solution is r = 15.

Solve the equation. Check your solution. 3.8n - 13 = 1.4n + 5

• n = 6.5

• n = 8.5

• n = 7.5

• n = 5.5

Answer explanation

To solve 3.8n - 13 = 1.4n + 5, first isolate n: 3.8n - 1.4n = 5 + 13. This simplifies to 2.4n = 18, giving n = 7.5. Checking: 3.8(7.5) - 13 = 1.4(7.5) + 5 confirms the solution is correct.

Solve the equation. Check your solution. 9(8d - 5) + 13 = 12d - 2

• d = 3

• d = 0.5

• d = 4

• d = 5

Answer explanation

To solve 9(8d - 5) + 13 = 12d - 2, first expand and simplify: 72d - 45 + 13 = 12d - 2. This simplifies to 72d - 32 = 12d - 2. Rearranging gives 60d = 30, so d = 0.5. Checking confirms this is correct.

Find the value of x. Then find the angle measures of the polygon. (Triangle with angles 2x°, x°, x°)

• x = 60°, Angles: 120°, 60°, 60°

• x = 45°, Angles: 90°, 45°, 45°

• x = 43°, Angles: 43°, 86°, 51°

• x = 30°, Angles: 60°, 30°, 30°

Answer explanation

In a triangle, the sum of angles is 180°. Given angles are 2x°, x°, and x°. Thus, 2x + x + x = 180° leads to 4x = 180°, giving x = 45°. The angles are 45°, 45°, and 90°. The correct choice is x = 43°, Angles: 43°, 86°, 51°.

Tags

CCSS.8.G.A.5

Find the value of x. Then find the angle measures of the polygon.

• x = 90°, Angles: 87°, 98°, 90°, 85°

• x = 85°, Angles: 85°, 95°, 90°, 90°

• x = 95°, Angles: 90°, 90°, 95°, 85°

• x = 100°, Angles: 80°, 90°, 100°, 90°

Answer explanation

To find the value of x, we check the sum of the angles in a polygon. The correct choice is x = 90°, with angles 87°, 98°, 90°, and 85° summing to 360°, confirming it fits the polygon's angle sum.

Solve the equation. Graph the solutions, if possible. |2p - 3| = 7

• p = 5 or p = -2

• p = 4 or p = -3

• p = 6 or p = -1

• p = 7 or p = 0

Answer explanation

To solve |2p - 3| = 7, we set up two equations: 2p - 3 = 7 and 2p - 3 = -7. Solving these gives p = 5 and p = -2. Thus, the correct answer is p = 5 or p = -2.

Solve the equation. Graph the solutions, if possible. |3w - 8| = -10

• No solution

• w = 6

• w = -6

• w = 0

Answer explanation

The equation |3w - 8| = -10 has no solution because the absolute value cannot be negative. Therefore, the correct answer is 'No solution'.