Sure! Let's solve each equation step by step.
### a. [tex]\(4x = 7 + 1\)[/tex]
1. Simplify the right-hand side:
[tex]\[
4x = 8
\][/tex]
2. Divide both sides by 4 to isolate [tex]\(x\)[/tex]:
[tex]\[
x = \frac{8}{4} = 2
\][/tex]
So, the solution for [tex]\( x \)[/tex] in equation (a) is [tex]\( x = 2 \)[/tex].
### b. [tex]\(2(x + 2) = 14\)[/tex]
1. Expand the left-hand side:
[tex]\[
2x + 4 = 14
\][/tex]
2. Subtract 4 from both sides to isolate the term with [tex]\(x\)[/tex]:
[tex]\[
2x = 10
\][/tex]
3. Divide both sides by 2 to solve for [tex]\(x\)[/tex]:
[tex]\[
x = \frac{10}{2} = 5
\][/tex]
So, the solution for [tex]\( x \)[/tex] in equation (b) is [tex]\( x = 5 \)[/tex].
### c. [tex]\(3x^2 = 27\)[/tex]
1. Divide both sides by 3 to simplify:
[tex]\[
x^2 = \frac{27}{3} = 9
\][/tex]
2. Take the square root of both sides:
[tex]\[
x = \sqrt{9} = \pm 3
\][/tex]
So, the solutions for [tex]\( x \)[/tex] in equation (c) are [tex]\( x = 3 \)[/tex] and [tex]\( x = -3 \)[/tex].
### d. [tex]\(\frac{33}{3x - 2} = 5.5\)[/tex]
1. Recognize that 5.5 can be written as a fraction:
[tex]\[
5.5 = \frac{11}{2}
\][/tex]
So, rewrite the equation:
[tex]\[
\frac{33}{3x - 2} = \frac{11}{2}
\][/tex]
2. Cross-multiply to clear the fraction:
[tex]\[
33 \times 2 = 11 \times (3x - 2)
\][/tex]
[tex]\[
66 = 33x - 22
\][/tex]
3. Add 22 to both sides to isolate the term with [tex]\(x\)[/tex]:
[tex]\[
88 = 33x
\][/tex]
4. Divide both sides by 33 to solve for [tex]\(x\)[/tex]:
[tex]\[
x = \frac{88}{33} = \frac{8}{3}
\][/tex]
So, the solution for [tex]\( x \)[/tex] in equation (d) is [tex]\( x = \frac{8}{3} \)[/tex].
### Summary:
- The solution for (a) is [tex]\( x = 2 \)[/tex].
- The solution for (b) is [tex]\( x = 5 \)[/tex].
- The solutions for (c) are [tex]\( x = 3 \)[/tex] and [tex]\( x = -3 \)[/tex].
- The solution for (d) is [tex]\( x = \frac{8}{3} \)[/tex].
