Sure, let's solve each equation step-by-step.
### 3. [tex]\( 2x + 1 = 5 \)[/tex]
First, we will isolate [tex]\( x \)[/tex].
1. Subtract 1 from both sides:
[tex]\[
2x + 1 - 1 = 5 - 1
\][/tex]
2. Simplify:
[tex]\[
2x = 4
\][/tex]
3. Divide both sides by 2:
[tex]\[
x = \frac{4}{2}
\][/tex]
4. Simplify:
[tex]\[
x = 2
\][/tex]
So, the solution to [tex]\( 2x + 1 = 5 \)[/tex] is [tex]\( x = 2 \)[/tex].
### 4. [tex]\( 2x = -3 + x \)[/tex]
Next, we will solve for [tex]\( x \)[/tex] by isolating it on one side of the equation.
1. Subtract [tex]\( x \)[/tex] from both sides:
[tex]\[
2x - x = -3 + x - x
\][/tex]
2. Simplify:
[tex]\[
x = -3
\][/tex]
So, the solution to [tex]\( 2x = -3 + x \)[/tex] is [tex]\( x = -3 \)[/tex].
### 5. [tex]\( 3 + 4(x - 2) = 7 \)[/tex]
Now let's solve for [tex]\( x \)[/tex].
1. Distribute the 4 inside the parentheses:
[tex]\[
3 + 4x - 8 = 7
\][/tex]
2. Combine like terms on the left-hand side:
[tex]\[
4x - 5 = 7
\][/tex]
3. Add 5 to both sides to isolate the term with [tex]\( x \)[/tex]:
[tex]\[
4x - 5 + 5 = 7 + 5
\][/tex]
4. Simplify:
[tex]\[
4x = 12
\][/tex]
5. Divide both sides by 4:
[tex]\[
x = \frac{12}{4}
\][/tex]
6. Simplify:
[tex]\[
x = 3
\][/tex]
So the solution to [tex]\( 3 + 4(x - 2) = 7 \)[/tex] is [tex]\( x = 3 \)[/tex].
### Summary of Solutions:
- [tex]\( 2x + 1 = 5 \)[/tex] has the solution [tex]\( x = 2 \)[/tex].
- [tex]\( 2x = -3 + x \)[/tex] has the solution [tex]\( x = -3 \)[/tex].
- [tex]\( 3 + 4(x - 2) = 7 \)[/tex] has the solution [tex]\( x = 3 \)[/tex].
