How to Solve the One-Variable Linear Equation 4x = 28

$Math Problem$

Mathematics Grade 5 (Primary School)

Question Content

Solve the equation 4x = 28

Correct Answer

x = 7

Detailed Solution Steps

1
Step 1: To solve for the variable x, we need to isolate it on one side of the equation. Since x is multiplied by 4, we perform the inverse operation, which is division, on both sides of the equation.
2
Step 2: Divide both sides of the equation by 4: (4x)/4 = 28/4
3
Step 3: Simplify both sides. On the left side, 4 divided by 4 cancels out, leaving x. On the right side, 28 divided by 4 equals 7. So x = 7.

Knowledge Points Involved

One-variable linear equation

A one-variable linear equation is an equation that can be written in the form ax + b = 0, where a and b are constants and a ≠ 0. In this problem, it is in the simplified form ax = c. It is used to represent and solve real-world or mathematical problems with a single unknown quantity.

Inverse operations

Inverse operations are pairs of operations that undo each other. Multiplication and division are inverse operations. When solving equations, we use inverse operations to isolate the variable, ensuring that we maintain equality by performing the same operation on both sides of the equation.

Equality property of equations

The equality property states that if we perform the same arithmetic operation (addition, subtraction, multiplication, division by a non-zero number) on both sides of an equal sign, the equality still holds. This is the core rule for solving all algebraic equations, as it allows us to manipulate the equation to find the value of the unknown variable.

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