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Lesson · Grade 8 · Mathematics

Algebra Tiles: Solving 2x + 3 = −5 with Zero Pairs

  • Grade 8
  • Mathematics
  • 1 min 59 s
  • British Columbia
  • BC8-MA-23

Algebra tiles model 2x + 3 = −5, and adding three negative tiles to both sides makes zero pairs that cancel, which leaves 2x = −8. Sharing both sides into two equal groups gives x = −4, which is checked by putting it back in: 2(−4) + 3 = −5.

Concept: Algebra tiles: solving an equation with zero pairs

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In one sentence

The question this lesson answers

Let us solve two x plus three equals negative five with algebra tiles, shapes that stand for amounts.

Here x is the variable, an unknown number. Two is its coefficient, so two x means two times x.

Transcript

What the lesson says

Let us solve two x plus three equals negative five with algebra tiles, shapes that stand for amounts.

Here x is the variable, an unknown number. Two is its coefficient, so two x means two times x.

A green x-tile is x, a yellow positive unit tile is one, and a red negative unit tile is negative one.

On the mat, the left side is two x-tiles and three positive unit tiles.

The right side is five negative unit tiles, for negative five.

The two sides are equal, so whatever we do to one side, we must do to the other.

To get the x-tiles alone, add three negative unit tiles to both sides.

A common mistake is changing tiles on one side only. Then the sides are no longer equal.

One positive tile and one negative tile make a zero pair, because one plus negative one is zero.

The left side has one, two, three zero pairs.

Each zero pair is worth zero, so take them away. Two x is left.

On the right, negative five plus negative three makes negative eight. So two x equals negative eight.

Two is the coefficient, so share each side into two equal groups. That divides both sides by two.

Each group has one x-tile and four negative unit tiles, so x equals negative four.

Check: two times negative four is negative eight, and negative eight plus three is negative five. It works.

Recap: do the same to both sides, remove zero pairs, then share into equal groups.

Curriculum

Where this fits

British Columbia, Grade 8

Mathematics, Patterns and algebra: two-step equations with integer coefficients, constants, and solutionsBC8-MA-23

Previous: Solving Two-Step Equations with Negative Numbers

The outcomes and strands follow the British Columbia curriculum.

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