Algebra

-3x + 5 = 23

Step-by-step solution with explanation

Final Answer

Step-by-step solution

Identify the equation to solve

We want to find the value of x that makes both sides equal. We'll isolate x by undoing the operations around it.

Subtract 5 from both sides

We subtract 5 from both sides to cancel the +5 on the left. Whatever we do to one side, we must do to the other to keep the equation balanced.

Simplify both sides

On the left, 5 - 5 = 0, leaving just -3x. On the right, 23 - 5 = 18.

Divide both sides by -3

We divide both sides by -3 to get x alone. Dividing by the coefficient of x isolates the variable.

Simplify to find x

On the left, -3 divided by -3 equals 1, leaving just x. On the right, 18 divided by -3 equals -6.

Understanding this problem

Learning Insight

This is a two-step linear equation. The word 'linear' means x has no exponent — it's just multiplied by a number. To solve it, we use inverse operations (opposites): subtraction undoes addition, and division undoes multiplication. We work in reverse order of PEMDAS — undoing addition/subtraction first, then multiplication/division.

Quick Tip

Always move the plain number (constant) first, then deal with the coefficient of x. Think of it as peeling layers off x from the outside in.

Common Mistake

Students often forget to flip the sign of the answer when dividing by a negative number. Dividing 18 by -3 gives -6, not +6. A positive divided by a negative is always negative.