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Lesson · Grade 8 · Mathematics

Solving Two-Step Equations with Negative Numbers

  • Grade 8
  • Mathematics
  • 2 min 17 s
  • British Columbia
  • BC8-MA-22

The video solves 3x − 4 = −13 by undoing its two steps in reverse order: add 4 to both sides, then divide by 3, and it checks that x = −3 makes both sides equal. It then solves −2x + 5 = 11, shows why you must divide by −2 and keep the sign, and checks the answer.

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In one sentence

The question this lesson answers

Let us solve 3x minus 4 equals negative 13.

The solution of an equation is the value of x that makes both sides equal.

Transcript

What the lesson says

Let us solve 3x minus 4 equals negative 13.

The solution of an equation is the value of x that makes both sides equal.

x is the variable, the unknown. 3 is the coefficient: it multiplies x. Negative 4 is a constant: a number on its own.

x was multiplied by 3, then 4 was subtracted. Inverse operations undo them in reverse order: add 4, then divide by 3.

Step 1: add 4 to both sides, so they stay equal.

Negative 4 plus 4 is 0, and negative 13 plus 4 is negative 9. So 3x equals negative 9.

Step 2: 3x means 3 times x, so divide both sides by 3.

Negative 9 divided by 3 is negative 3, since a negative divided by a positive is negative. So x equals negative 3.

Put in negative 3: 3 times negative 3 is negative 9, and negative 9 minus 4 is negative 13. It matches.

Now a negative coefficient: negative 2x plus 5 equals 11.

Step 1: subtract 5 from both sides. 11 minus 5 is 6, so negative 2x equals 6.

Step 2: divide both sides by negative 2, keeping the sign.

6 divided by negative 2 is negative 3, since a positive divided by a negative is negative. So x equals negative 3.

A common mistake is to lose the sign and get x equals 3. But negative 2 times 3, plus 5, is negative 1, not 11.

Check negative 3: negative 2 times negative 3 is 6, and 6 plus 5 is 11. It matches.

To recap: undo adding or subtracting first, then divide by the coefficient, sign and all.

Curriculum

Where this fits

British Columbia, Grade 8

Mathematics, Patterns and algebra: two-step equations with integer coefficients, constants, and solutionsBC8-MA-22

Previous: Substituting into Expressions with Negatives and DecimalsNext: Algebra Tiles: Solving 2x + 3 = −5 with Zero Pairs

The outcomes and strands follow the British Columbia curriculum.

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