Question

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Answer 1

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Answer 2

Solving the Equations

To solve the equations 8+4x > 0 and 4-3x > -8, we need to find the values of x that satisfy both inequalities.

Let's solve each equation separately:

Equation 1: 8+4x > 0

To solve this equation, we need to isolate x on one side of the inequality sign. Here's the step-by-step process:

1. Subtract 8 from both sides of the equation: 8 + 4x - 8 > 0 - 8 Simplifying, we get: 4x > -8

2. Divide both sides of the equation by 4: (4x)/4 > (-8)/4 Simplifying, we get: x > -2

Therefore, the solution to the equation 8+4x > 0 is x > -2.

Equation 2: 4-3x > -8

To solve this equation, we'll follow a similar process:

1. Add 8 to both sides of the equation: 4 - 3x + 8 > -8 + 8 Simplifying, we get: -3x + 12 > 0

2. Subtract 12 from both sides of the equation: -3x + 12 - 12 > 0 - 12 Simplifying, we get: -3x > -12

3. Divide both sides of the equation by -3. Since we're dividing by a negative number, the inequality sign will flip: (-3x)/-3 < (-12)/-3 Simplifying, we get: x < 4

Therefore, the solution to the equation 4-3x > -8 is x < 4.

Combined Solution

To find the values of x that satisfy both inequalities, we need to find the intersection of the solution sets.

From the first equation, we have x > -2, and from the second equation, we have x < 4.

The overlapping region between x > -2 and x < 4 is -2 < x < 4.

Therefore, the solution to the system of equations 8+4x > 0 and 4-3x > -8 is -2 < x < 4.

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