Question

place the correct option to complete the sentence.
$\boxed{}$ $x = -\frac{11}{2}$ $\boxed{}$ $x = -\frac{7}{2}$ $\boxed{}$ $x = \frac{1}{2}$ $\boxed{}$ $x = \frac{5}{2}$
the solution to the equation $2x = 4(x - 2) + 3$ is

Explanation:

Step1: Expand the right side

Expand \(4(x - 2)+3\) to get \(4x-8 + 3=4x-5\). So the equation becomes \(2x=4x - 5\).

Step2: Move terms with \(x\)

Subtract \(2x\) from both sides: \(0 = 2x-5\). Then add \(5\) to both sides: \(2x = 5\).

Step3: Solve for \(x\)

Divide both sides by \(2\): \(x=\frac{5}{2}\)? Wait, no, wait. Wait, original equation: \(2x=4(x - 2)+3\). Let's redo:

Expand \(4(x - 2)+3\): \(4x-8 + 3=4x-5\). So \(2x=4x - 5\). Subtract \(2x\) from both sides: \(0 = 2x-5\). Then add \(5\): \(2x=5\)? No, wait, subtract \(4x\) from both sides: \(2x-4x=-5\) → \(-2x=-5\) → \(x=\frac{5}{2}\)? Wait, but the options have \(x = \frac{5}{2}\)? Wait, the options: let's check the equation again. Wait, maybe I misread the equation. Wait, the equation is \(2x = 4(x - 2)+3\)? Wait, maybe the equation is \(2x=4(x - 2)+3\)? Let's solve again:

\(2x=4x-8 + 3\) → \(2x=4x-5\) → \(2x-4x=-5\) → \(-2x=-5\) → \(x=\frac{5}{2}\). Wait, but the options: the last option is \(x=\frac{5}{2}\)? Wait, but let's check the options again. Wait, the options are:

1. \(x = -\frac{11}{2}\)

1. \(x = -\frac{7}{2}\)

1. \(x=\frac{1}{2}\)

1. \(x=\frac{5}{2}\)

Wait, so solving \(2x = 4(x - 2)+3\):

\(2x=4x-8 + 3\)

\(2x=4x-5\)

\(2x-4x=-5\)

\(-2x=-5\)

\(x=\frac{5}{2}\). So the correct option is the fourth one, \(x = \frac{5}{2}\). Wait, but maybe the equation was different? Wait, maybe the equation is \(2x=4(x - 2)+3\)? Yes. So the solution is \(x=\frac{5}{2}\), which is the fourth option.

Wait, but let's check again. Let's plug \(x=\frac{5}{2}\) into the original equation:

Left side: \(2\times\frac{5}{2}=5\).

Right side: \(4(\frac{5}{2}-2)+3=4(\frac{1}{2})+3=2 + 3=5\). So it works. So the correct option is the one with \(x=\frac{5}{2}\).

Answer:

The correct option is the fourth one (assuming the options are ordered as given: the last option) with \(x=\frac{5}{2}\). If the options are labeled as, say, A: \(x = -\frac{11}{2}\), B: \(x = -\frac{7}{2}\), C: \(x=\frac{1}{2}\), D: \(x=\frac{5}{2}\), then the answer is D. \(x=\frac{5}{2}\)