Math Problem Statement

Solve the following equations: (i) 17 - 28 = k + 5, (j) (5m/4) = -15, (k) (m - 6)/2 = 4, (l) k/5 - 10 = 2, (m) 4 + h/5 = 6, (n) 2(x + 2) = 6, (o) -(d + 3) = 11

Solution

I see you've uploaded an image containing several equations. Let's go through them step by step.

(i) Solve:

1728=k+517 - 28 = k + 5 First, simplify the left-hand side: 1728=1117 - 28 = -11 Now we have: 11=k+5-11 = k + 5 To solve for kk, subtract 5 from both sides: k=115=16k = -11 - 5 = -16 So, k=16k = -16.


(j) Solve:

5m4=15\frac{5m}{4} = -15 First, multiply both sides by 4 to get rid of the fraction: 5m=15×4=605m = -15 \times 4 = -60 Now divide both sides by 5: m=605=12m = \frac{-60}{5} = -12 So, m=12m = -12.


(k) Solve:

m62=4\frac{m - 6}{2} = 4 Multiply both sides by 2: m6=4×2=8m - 6 = 4 \times 2 = 8 Now, add 6 to both sides: m=8+6=14m = 8 + 6 = 14 So, m=14m = 14.


(l) Solve:

k510=2\frac{k}{5} - 10 = 2 First, add 10 to both sides: k5=2+10=12\frac{k}{5} = 2 + 10 = 12 Now, multiply both sides by 5: k=12×5=60k = 12 \times 5 = 60 So, k=60k = 60.


(m) Solve:

4+h5=64 + \frac{h}{5} = 6 First, subtract 4 from both sides: h5=64=2\frac{h}{5} = 6 - 4 = 2 Now, multiply both sides by 5: h=2×5=10h = 2 \times 5 = 10 So, h=10h = 10.


(n) Solve:

2(x+2)=62(x + 2) = 6 First, divide both sides by 2: x+2=62=3x + 2 = \frac{6}{2} = 3 Now, subtract 2 from both sides: x=32=1x = 3 - 2 = 1 So, x=1x = 1.


(o) Solve:

(d+3)=11-(d + 3) = 11 First, multiply both sides by -1: d+3=11d + 3 = -11 Now, subtract 3 from both sides: d=113=14d = -11 - 3 = -14 So, d=14d = -14.


Would you like any further explanation or details on any step? Here are some related questions:

  1. Can you explain how to solve linear equations step-by-step?
  2. How would these problems change if they involved fractions or decimals?
  3. What happens if variables appear on both sides of an equation?
  4. How would you solve an equation with two variables?
  5. What are common mistakes to avoid when solving linear equations?

Tip: Always check your solution by substituting the value back into the original equation to see if both sides are equal!

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Solving for Variables

Formulas

Basic linear equation: ax + b = c
Isolating variables using inverse operations
Multiplying/dividing to eliminate fractions

Theorems

Properties of equality (adding, subtracting, multiplying, dividing both sides of an equation)

Suitable Grade Level

Grades 6-8