5. 4x + 2 = x + 8. (1 point) x = 4 x = 3 x = 2 x = 1 Solve the inequality. 6. q – 12 ≥ –13 (1 point) q ≥ 1 q ≥ –1 q ≥ 25 q ≥ –25 7. 12p < 96 (1 point) p < 8 p < 108 p < 84 p < –8 8. < –18 (1 point) g < –23 g > –90 g > 90 g < 90 9. Write the inequality and solve for the following problem: The result of 6 subtracted from a number n is at least 2. (1 point) n – 2 > 6; n > 8 n – 6 ≥ 2; n ≥ 8 n + 6 ≥ 2; n ≤ 4 n + 6 ≥ 2; n ≥ 4
To solve these algebraic problems and inequalities, we can follow a step-by-step approach. Let's go through each question and explain the process.
5. 4x + 2 = x + 8:
To solve this equation, we need to isolate the variable x on one side. We can do this by performing inverse operations to eliminate terms. Here's the step-by-step process:
4x + 2 = x + 8
Subtract x from both sides:
4x - x + 2 = x - x + 8
3x + 2 = 8
Subtract 2 from both sides:
3x + 2 - 2 = 8 - 2
3x = 6
Divide both sides by 3:
(3x)/3 = 6/3
x = 2
Therefore, the answer is x = 2.
6. q – 12 ≥ –13:
To solve this inequality, we need to isolate the variable q on one side. Here's the step-by-step process:
q - 12 ≥ -13
Add 12 to both sides:
q - 12 + 12 ≥ -13 + 12
q ≥ -1
Therefore, the answer is q ≥ -1.
7. 12p < 96:
To solve this inequality, we need to isolate the variable p on one side. Here's the step-by-step process:
12p < 96
Divide both sides by 12 (since it's a positive number):
(12p)/12 < 96/12
p < 8
Therefore, the answer is p < 8.
8. g < -18:
To solve this inequality, we can leave it as is since there are no additional operations needed. The answer is already provided.
Therefore, the answer is g < -18.
9. The result of 6 subtracted from a number n is at least 2.
To write and solve the inequality, we can follow these steps:
n - 6 ≥ 2
Add 6 to both sides:
n - 6 + 6 ≥ 2 + 6
n ≥ 8
Therefore, the answer is n ≥ 8.