Math  /  Algebra

Question4) 8c184<4(35c)8 c-184<4(3-5 c) 9) 4a6+5a1474 a-6+5 a \geq 147

Studdy Solution

STEP 1

1. Both problems involve solving linear inequalities.
2. We will isolate the variable on one side of the inequality.
3. We will perform algebraic operations to simplify the inequalities.
4. We will consider the properties of inequalities, such as reversing the inequality sign when multiplying or dividing by a negative number.

_HIGH_LEVEL_APPROACH_ for Problem 4:
1. Simplify both sides of the inequality.
2. Combine like terms and isolate the variable.
3. Solve the inequality for the variable.

_HIGH_LEVEL_APPROACH_ for Problem 9:
1. Combine like terms on one side of the inequality.
2. Isolate the variable.
3. Solve the inequality for the variable.

**Problem 4:**

STEP 2

STEP 3

Simplify the right-hand side of the inequality 8c184<4(35c) 8c - 184 < 4(3 - 5c) .
Distribute the 4:
8c184<1220c 8c - 184 < 12 - 20c

STEP 4

Add 20c 20c to both sides to begin isolating the variable:
8c+20c184<12 8c + 20c - 184 < 12
Combine like terms:
28c184<12 28c - 184 < 12

STEP 5

Add 184 to both sides to further isolate the variable term:
28c<196 28c < 196
Divide both sides by 28:
c<7 c < 7
**Problem 9:**
STEP_1:
Combine like terms on the left-hand side of the inequality 4a6+5a147 4a - 6 + 5a \geq 147 .
(4a+5a)6147 (4a + 5a) - 6 \geq 147
Combine like terms:
9a6147 9a - 6 \geq 147
STEP_2:
Add 6 to both sides to isolate the variable term:
9a153 9a \geq 153
STEP_3:
Divide both sides by 9 to solve for a a :
a17 a \geq 17
The solutions are: For Problem 4: c<7 c < 7 For Problem 9: a17 a \geq 17

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