Equation 1. $$ (2 x+3=4(x-1)+5) $$

Question

UpStudy AI · Accepted Answer

Sure, let's solve the equation step by step:

$$
2x + 3 = 4(x - 1) + 5
$$

### Step 1: Expand the Right Side

First, distribute the $$4$$ on the right side of the equation:

$$
2x + 3 = 4 \cdot x - 4 \cdot 1 + 5
$$
$$
2x + 3 = 4x - 4 + 5
$$

Combine like terms on the right side:

$$
2x + 3 = 4x + 1
$$

### Step 2: Bring Like Terms Together

Subtract $$2x$$ from both sides to get all the $$x$$-terms on one side:

$$
2x + 3 - 2x = 4x + 1 - 2x
$$
$$
3 = 2x + 1
$$

Next, subtract $$1$$ from both sides to isolate the term with $$x$$:

$$
3 - 1 = 2x + 1 - 1
$$
$$
2 = 2x
$$

### Step 3: Solve for $$x$$

Divide both sides by $$2$$ to solve for $$x$$:

$$
\frac{2}{2} = \frac{2x}{2}
$$
$$
1 = x
$$

### Solution

$$
x = 1
$$
$$ x = 1 $$

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