Math Problem Statement

A series of algebraic problems covering solving equations, finding roots, and applications in word problems, as shown in the uploaded image.

Solution

I can see the mathematical problems you uploaded. I will solve these questions for you. Let me start systematically.


Level 1

1. Solve these equations:

  • (a) 3(x + 1) = 15
    Expand: 3x+3=153x + 3 = 15
    Solve for xx:
    3x=153=12    x=123=43x = 15 - 3 = 12 \implies x = \frac{12}{3} = 4 Answer: (a) x=4x = 4

  • (b) 2(x + 4) = -10
    Expand: 2x+8=102x + 8 = -10
    Solve for xx:
    2x=108=18    x=182=92x = -10 - 8 = -18 \implies x = \frac{-18}{2} = -9 Answer: (b) x=9x = -9

  • (c) 4x - 9 = 8
    Solve for xx:
    4x=8+9=17    x=1744x = 8 + 9 = 17 \implies x = \frac{17}{4} Answer: (c) x=174x = \frac{17}{4}

  • (d) -3(x - 1) = -12
    Expand: 3x+3=12-3x + 3 = -12
    Solve for xx:
    3x=123=15    x=153=5-3x = -12 - 3 = -15 \implies x = \frac{-15}{-3} = 5 Answer: (d) x=5x = 5


2. Find the roots of these equations:

  • (a) 3(y + 1) = 21
    Expand: 3y+3=213y + 3 = 21
    Solve for yy:
    3y=213=18    y=183=63y = 21 - 3 = 18 \implies y = \frac{18}{3} = 6 Answer: y=6y = 6

  • (b) 5(y - 4) = 25
    Expand: 5y20=255y - 20 = 25
    Solve for yy:
    5y=25+20=45    y=455=95y = 25 + 20 = 45 \implies y = \frac{45}{5} = 9 Answer: y=9y = 9

  • (c) 7(y - 2) = 42
    Expand: 7y14=427y - 14 = 42
    Solve for yy:
    7y=42+14=56    y=567=87y = 42 + 14 = 56 \implies y = \frac{56}{7} = 8 Answer: y=8y = 8

  • (d) 5(3x) = 60
    Solve for xx:
    15x=60    x=6015=415x = 60 \implies x = \frac{60}{15} = 4 Answer: x=4x = 4


Would you like me to continue solving Level 2 problems or any specific question?

Here are 5 related questions for practice:

  1. Solve 4(2x5)=124(2x - 5) = 12.
  2. Find the value of xx in 3(x4)+2=113(x - 4) + 2 = 11.
  3. Solve for xx: 7(3x+2)=427(3x + 2) = 42.
  4. If 5(2y1)=155(2y - 1) = 15, what is yy?
  5. Solve 6x7=2x+216x - 7 = 2x + 21.

Tip: Always simplify and isolate the variable step by step!

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Word Problems
Equation Roots

Formulas

General linear equation formula ax + b = c
Equation manipulation rules (e.g., isolate variables, expand brackets)
Word problem modeling with variables

Theorems

Basic properties of equality
Distributive property (a(b + c) = ab + ac)
Arithmetic principles in equation solving

Suitable Grade Level

Grades 6-9