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Two-Step Linear Equations

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Two-Step Linear Equations

Solve each two-step equation to find its code or value. Undo addition or subtraction first, then undo multiplication or division. Show each step and check by substituting your answer into the original equation.

Find the correct moves

Warm up with inverse operations, then solve the first lock.

1.For 4x + 7 = 31, which operation should you use first to isolate the term containing x?

Add 7 to both sides
Subtract 7 from both sides
Divide both sides by 4
Multiply both sides by 4

2.Solve the first lock: 4x + 7 = 31. Write the two inverse-operation steps and the value of x.

3.A control panel displays 3y − 8 = 19. Complete the solution: add to both sides, giving 3y = ; then divide by , so y = .

Solve and verify

The next locks use division, negatives and decimals. Remember to reverse the order of operations.

4.Solve 2a + 5 = 17, then check your answer by substituting it into the original equation.

5.Solve n/5 − 3 = 4. Show how you undo the subtraction and then the division.

6.For 5p − 4 = 21, does dividing both sides by 5 immediately isolate p? State the more direct first step and solve the equation.

7.A challenge lock reads 0.5m + 3 = 7. Solve for m and show both steps.

Equations in the real world

Write an equation from each situation before solving it.

8.A whānau buys 3 identical reusable drink bottles and pays a $6 delivery fee. The total is $42. Let b be the price of one bottle. Write an equation and find b.

9.A hiking track is 18 km long. Hana has already walked 4 km, then walks the same distance d on each of 2 more sections. Write an equation for the total distance and find d.

10.Create a two-step equation with solution x = 4. Use the form ax + b = c, where a is not zero, then show a check.