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Solve Real-World and Mathematical Problems by Writing and Solving Equations

Show all steps. Always verify your solution by substituting it back into the original equation.

Grade 6·21 problems·~35 min·Common Core Math - Grade 6·standard·6-ee-b-7
Work through problems with immediate feedback
A

Recall / Warm-Up

1.

If x+5=12x + 5 = 12, which operation should be applied to isolate xx?

2.

Which equation fits the structure px=qpx = q?

B

Fluency Practice

1.

Solve x+3=11x + 3 = 11.

2.

Solve n+6.5=14n + 6.5 = 14.

3.

Solve 43+y=2\frac{4}{3} + y = 2.

4.

Solve 4x=284x = 28.

5.

Solve 3n=7.53n = 7.5.

C

Varied Practice

Two balance scales showing x plus 8 balanced against 20, then the same equation after subtracting 8 from both sides without simplifying to the final answer.
1.

Solve x+8=20x + 8 = 20 using inverse operations.

The inverse of adding 8 is   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   .

Applying it to both sides: x=20−x = 20 -   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   ==   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   .

inverse operation:
value subtracted:
solution:
2.

Which is the correct first step to solve x+14=25x + 14 = 25?

3.

Solve 6x=426x = 42.

Divide both sides by   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   : x=42÷x = 42 \div   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   ==   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   .

divisor:
divisor (check):
solution:
4.

Solve 23x=4\frac{2}{3}x = 4.

5.

Which equation, when solved, gives x=9x = 9?

D

Word Problems / Application

1.

Emma spent $12.50 on lunch, leaving her with $7.25. Let xx represent how much Emma started with.

1.

Which equation represents this situation?

2.

Solve the equation and find how much Emma started with.

2.

A recipe uses 23\frac{2}{3} cup of oil per batch. How many batches can be made from 4 cups of oil?

The equation is   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   .

The number of batches is   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   .

equation:
number of batches:
3.

A bag of fertilizer covers 5 square meters. A garden has 35 square meters to cover. Which equation finds bb, the number of bags needed?

E

Error Analysis

1.

Raj solved x+5=12x + 5 = 12 and got x=5−12=−7x = 5 - 12 = -7.

What error did Raj make?

2.

Sofia solved 6x=426x = 42 and got x=642=17x = \frac{6}{42} = \frac{1}{7}.

What error did Sofia make?

3.

A word problem says: 'Miguel spent $15 at the store and had $8 left.' Carlos wrote the equation 15−x=815 - x = 8 to find how much Miguel started with.

What error did Carlos make in setting up the equation?

F

Challenge

1.

A truck can carry a load of 34\frac{3}{4} ton per trip. After several trips, it has carried 6 tons total. How many trips did the truck make?

2.

Write a word problem that can be solved with the equation n4=7\frac{n}{4} = 7. Then solve and verify.

0 of 21 answered