Math Problem Statement

Solve the following algebraic equations: 1) 2x + 150 = 32x 2) -x + 10 = 3x 3) -2x - 28 = 5x 4) 4x - 6x = 4(x - 3) 5) x - (2x + 4) = 4x + 6 6) 5(2x + 4) = 6(3x + 2) 7) 15x - 9(13 + x) = -6(21 - 2x)

Solution

It looks like the document you've shared contains a series of algebraic equations that need to be solved, presented in Hebrew. Here's the list of equations from the image, with the task to solve them:

  1. 2x+150=32x2x + 150 = 32x
  2. x+10=3x-x + 10 = 3x
  3. 2x28=5x-2x - 28 = 5x
  4. 4x6x=4(x3)4x - 6x = 4(x - 3)
  5. x(2x+4)=4x+6x - (2x + 4) = 4x + 6
  6. 5(2x+4)=6(3x+2)5(2x + 4) = 6(3x + 2)
  7. 15x9(13+x)=6(212x)15x - 9(13 + x) = -6(21 - 2x)

Let me solve these equations step by step.

1) 2x+150=32x2x + 150 = 32x

2x+150=32x2x + 150 = 32x Subtract 2x2x from both sides: 150=30x150 = 30x Divide both sides by 30: x=15030=5x = \frac{150}{30} = 5

2) x+10=3x-x + 10 = 3x

x+10=3x-x + 10 = 3x Add xx to both sides: 10=4x10 = 4x Divide both sides by 4: x=104=2.5x = \frac{10}{4} = 2.5

3) 2x28=5x-2x - 28 = 5x

2x28=5x-2x - 28 = 5x Add 2x2x to both sides: 28=7x-28 = 7x Divide both sides by 7: x=287=4x = \frac{-28}{7} = -4

4) 4x6x=4(x3)4x - 6x = 4(x - 3)

4x6x=4(x3)4x - 6x = 4(x - 3) Simplify both sides: 2x=4x12-2x = 4x - 12 Subtract 4x4x from both sides: 6x=12-6x = -12 Divide both sides by 6-6: x=126=2x = \frac{-12}{-6} = 2

5) x(2x+4)=4x+6x - (2x + 4) = 4x + 6

x(2x+4)=4x+6x - (2x + 4) = 4x + 6 Distribute the minus sign: x2x4=4x+6x - 2x - 4 = 4x + 6 Simplify: x4=4x+6-x - 4 = 4x + 6 Add xx to both sides: 4=5x+6-4 = 5x + 6 Subtract 6 from both sides: 10=5x-10 = 5x Divide both sides by 5: x=105=2x = \frac{-10}{5} = -2

6) 5(2x+4)=6(3x+2)5(2x + 4) = 6(3x + 2)

Distribute on both sides: 10x+20=18x+1210x + 20 = 18x + 12 Subtract 10x10x from both sides: 20=8x+1220 = 8x + 12 Subtract 12 from both sides: 8=8x8 = 8x Divide by 8: x=1x = 1

7) 15x9(13+x)=6(212x)15x - 9(13 + x) = -6(21 - 2x)

Distribute on both sides: 15x9(13+x)=6(212x)15x - 9(13 + x) = -6(21 - 2x) Simplify: [ 15x - 117 - 9x = -126 +

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Simplification
Equation Solving

Formulas

Basic linear equation formulas
Distributive property: a(b + c) = ab + ac

Theorems

Properties of equality
Distributive property

Suitable Grade Level

Grades 8-10