How to Solve $ 4x - 7 = 89 $: A Simple Step-by-Step Guide

Solving linear equations like $ 4x - 7 = 89 $ is an essential math skill used in classrooms, science, and real-world problem solving. Whether you're a student learning algebra or someone brushing up on fundamentals, understanding how to isolate variables step by step makes math easier and more intuitive.

In this article, we’ll break down how to solve the equation $ 4x - 7 = 89 $ in simple, clear terms so you can confidently work through similar problems.

Understanding the Context

What is the Equation $ 4x - 7 = 89 $?

The equation $ 4x - 7 = 89 $ is a linear equation containing one variable, $ x $. Our goal is to find the value of $ x $ that makes the equation true.

Simplify: $ 4x - 7 = 89 $.

Key Insights

Step-by-Step Solution

Step 1: Eliminate the constant on the left side

Start by removing the $-7$ from the left side. To do this, add 7 to both sides of the equation:
$$
4x - 7 + 7 = 89 + 7
$$
Simplifying both sides gives:
$$
4x = 96
$$

Step 2: Solve for $ x $

Now, divide both sides by 4 to isolate $ x $:
$$
rac{4x}{4} = rac{96}{4}
$$
This simplifies to:
$$
x = 24
$$

Final Answer

Continue Reading

A developer is tasked with determining the maximum area of a rectangular plot with a fixed perimeter of 100 meters. What dimensions maximize the area, and what is the maximum area?
Let the length and width of the rectangle be \( l \) and \( w \) respectively. Given the perimeter is 100 meters:
This is a quadratic equation in the form \( -l^2 + 50l \). The maximum area occurs at the vertex of the parabola, \( l = -\frac{b}{2a} \), where \( a = -1 \) and \( b = 50 \):

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Final Thoughts

The solution to the equation $ 4x - 7 = 89 $ is $ x = 24 $. This means when $ x $ equals 24, the expression $ 4x - 7 $ equals 89.

Tips for Mastering Linear Equation Solving

  • Always perform the same operation on both sides of the equation to keep it balanced.
  • Begin by working toward isolating $ x $ — first eliminate constants, then deal with coefficients.
  • Always verify your answer by substituting $ x $ back into the original equation.
  • Practice regularly with diverse equations to build speed and accuracy.

Why This Equation Matters

Solving equations like $ 4x - 7 = 89 $ is more than just algebra — it builds logical thinking and problem-solving skills used in science, computer programming, finance, and engineering. Understanding these basics prepares you for advanced mathematics and real-life applications.

Summary

  • Original equation: $ 4x - 7 = 89 $
  • Subtract 7 from both sides: $ 4x = 96 $
  • Divide both sides by 4: $ x = 24 $
  • Solution verified: checks out in original equation
  • Practice = confidence!