https://file.aiquickdraw.com/mathbot/file/1726162210998p9l17ty8.jpg

I can see the equations clearly. Let's solve each one of them step by step:

### 1. \( 8x - 5x - 4 = 14 \)
Simplify the equation:
\[
(8x - 5x) - 4 = 14 \Rightarrow 3x - 4 = 14
\]
Add 4 to both sides:
\[
3x = 18
\]
Divide by 3:
\[
x = 6
\]

### 2. \( 34y - y + 11 = 110 \)
Simplify the equation:
\[
(34y - y) + 11 = 110 \Rightarrow 33y + 11 = 110
\]
Subtract 11 from both sides:
\[
33y = 99
\]
Divide by 33:
\[
y = 3
\]

### 3. \( -11a + 16a - 100 = 15 \)
Simplify the equation:
\[
(-11a + 16a) - 100 = 15 \Rightarrow 5a - 100 = 15
\]
Add 100 to both sides:
\[
5a = 115
\]
Divide by 5:
\[
a = 23
\]

### 4. \( b - \frac{b}{4} - 16 = -4 \)
To eliminate the fraction, multiply the entire equation by 4:
\[
4b - b - 64 = -16
\]
Simplify:
\[
3b - 64 = -16
\]
Add 64 to both sides:
\[
3b = 48
\]
Divide by 3:
\[
b = 16
\]

### 5. \( d + \frac{d}{18} + 3 = 22 \)
Subtract 3 from both sides:
\[
d + \frac{d}{18} = 19
\]
Multiply the entire equation by 18 to eliminate the fraction:
\[
18d + d = 342
\]
Simplify:
\[
19d = 342
\]
Divide by 19:
\[
d = 18
\]

### 6. \( \frac{234z}{500} - 3z - 1 = -1 \)
Add 1 to both sides:
\[
\frac{234z}{500} - 3z = 0
\]
Multiply the entire equation by 500 to eliminate the fraction:
\[
234z - 1500z = 0
\]
Simplify:
\[
-1266z = 0
\]
Divide by \(-1266\):
\[
z = 0
\]

---

If you have any questions or need further explanations, feel free to ask! Here are 5 related questions to expand your understanding:

1. How can you solve multi-step equations with variables on both sides?
2. What are the steps to isolate variables in equations with fractions?
3. How do you solve systems of linear equations with more than one unknown?
4. How can you solve quadratic equations through factoring or using the quadratic formula?
5. What is the difference between solving linear and non-linear equations?

**Tip**: Always combine like terms and eliminate fractions early in the process to simplify the solution path.

Solve the multi-step equations: 1. 8x - 5x - 4 = 14, 2. 34y - y + 11 = 110, 3. -11a + 16a - 100 = 15, 4. b - b/4 - 16 = -4, 5. d + d/18 + 3 = 22, 6. 234z/500 - 3z - 1 = -1

Step-by-step solution to multi-step algebraic equations, including linear equations with variables and fractions. Covers equations such as 8x - 5x - 4 = 14 and 34y - y + 11 = 110. Ideal for Grades 8-10 algebra practice.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation