Math Problem Statement

(¾)x + 1 = (½)x - 3

Solution

Let's solve the equation 34x+1=12x3\frac{3}{4}x + 1 = \frac{1}{2}x - 3.

Step-by-step Solution:

  1. Eliminate the fractions: Multiply the entire equation by 4, the least common denominator of 4 and 2, to eliminate the fractions: 4(34x+1)=4(12x3)4\left(\frac{3}{4}x + 1\right) = 4\left(\frac{1}{2}x - 3\right) Simplifying both sides: 3x+4=2x123x + 4 = 2x - 12

  2. Move xx-terms to one side: Subtract 2x2x from both sides: 3x2x+4=123x - 2x + 4 = -12 x+4=12x + 4 = -12

  3. Isolate xx: Subtract 4 from both sides: x=124x = -12 - 4 x=16x = -16

Final Answer:

x=16x = -16

Would you like further clarification or details on any step?

Related Questions:

  1. How do you solve equations with more complicated fractions?
  2. What are some tips for solving equations involving decimals?
  3. How do you solve equations with variables on both sides and constants?
  4. Can you explain how to handle equations with parentheses and fractions?
  5. What is the process for solving quadratic equations?

Tip:

When solving equations with fractions, clearing the denominators by multiplying through by the least common multiple makes the process much simpler.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Equations with Fractions

Formulas

Ax + B = C

Theorems

Basic Properties of Equality

Suitable Grade Level

Grades 6-8