Question

4(x - 2) - 5 ≥ -3(-2 + 7) + 3
4(x - 2) - 5 ≥
(type an integer or a fraction.)

Explanation:

Step1: Simplify both sides

First, expand the expressions. For the left side: \(4(x - 2)-5 = 4x-8 - 5=4x - 13\). For the right side: \(-3(-2 + 7)+3=-3\times5 + 3=-15 + 3=-12\). So the inequality becomes \(4x-13\geq - 12\).

Step2: Solve for x

Add 13 to both sides: \(4x-13 + 13\geq - 12+13\), which simplifies to \(4x\geq1\). Then divide both sides by 4: \(x\geq\frac{1}{4}\). Wait, maybe I misread the original inequality. Wait, the original problem: let's re - check. Wait, the user's problem: \(4(x - 2)-5\geq-3(-2 + 7)+3\)? Wait, no, maybe the second line is a typo? Wait, the first inequality is \(4(x - 2)-5\geq-3(-2 + 7)+3\)? Wait, let's re - do:

Wait, the right - hand side: \(-3(-2 + 7)+3=-3\times5 + 3=-15 + 3=-12\). Left - hand side: \(4(x - 2)-5 = 4x-8 - 5=4x-13\). So the inequality is \(4x-13\geq - 12\). Add 13 to both sides: \(4x\geq1\), then \(x\geq\frac{1}{4}\). But maybe the original problem is \(4(x - 2)-5\geq-3(-2x + 7)+3\)? Wait, the user's image: the second inequality line: \(4(x - 2)-5\geq-3(-2 + 7)+3\)? No, maybe a typo. Wait, maybe the right - hand side is \(-3(-2x + 7)+3\). Let's assume that (since otherwise the answer is \(x\geq\frac{1}{4}\), but maybe the original problem has a typo). Wait, if the right - hand side is \(-3(-2x + 7)+3\), then:

Left side: \(4(x - 2)-5=4x-8 - 5 = 4x-13\)

Right side: \(-3(-2x + 7)+3 = 6x-21 + 3=6x-18\)

Then the inequality is \(4x-13\geq6x-18\)

Subtract \(4x\) from both sides: \(-13\geq2x-18\)

Add 18 to both sides: \(5\geq2x\)

Divide by 2: \(x\leq\frac{5}{2}\)

But since the user's image is a bit unclear, but let's go back. Wait, the user's problem: the first inequality is \(4(x - 2)-5\geq-3(-2 + 7)+3\)? No, maybe the second line is a mistake. Wait, maybe the original problem is \(4(x - 2)-5\geq-3(-2x + 7)+3\). But given the user's input, maybe I made a mistake. Wait, let's re - examine the user's image:

The first line: \(4(x - 2)-5\geq - 3(-2 + 7)+3\)

Second line: \(4(x - 2)-5\geq\square\) (with a box) and "Type an integer or a fraction"

Wait, maybe the problem is to simplify the right - hand side first. Let's compute the right - hand side: \(-3(-2 + 7)+3=-3\times5 + 3=-15 + 3=-12\). So the inequality is \(4(x - 2)-5\geq - 12\). Then expand the left - hand side: \(4x-8 - 5\geq - 12\), so \(4x-13\geq - 12\). Add 13 to both sides: \(4x\geq1\), then \(x\geq\frac{1}{4}\).

Answer:

\(x\geq\frac{1}{4}\) (If the right - hand side is as calculated. If there is a typo in the original problem, the answer may change. But based on the given information, this is the solution.)