Solving Simple Equations

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ISEE Lower Level: Mathematics Achievement › Solving Simple Equations

Questions 1 - 10
1

A trip is fifteen miles, and you go five miles first. Solve for $x$: $5 + x = 15$.

fifteen

five

twenty

ten

Explanation

This question tests solving for an unknown in a simple equation (ISEE Lower Level Mathematics Achievement). Understanding simple equations involves isolating the variable to find its value. In the scenario '5 + x = 15', x represents the unknown number of miles remaining after traveling the first five miles of a fifteen-mile trip, and solving it involves subtracting 5 from both sides. Choice B is correct because it correctly identifies x as 10 when you isolate the variable by subtracting 5 from 15 (15 - 5 = 10). Choice A (fifteen) uses the total distance, Choice C (five) repeats the distance already traveled, and Choice D (twenty) results from adding 5 to 15. To help students: Draw a number line showing the 15-mile journey with 5 miles completed. Emphasize that x represents the remaining distance: 5 + 10 = 15 ✓.

2

You need $9$ cups of flour. You already have $4$ cups. Solve for $x$: $x + 4 = 9$.

5

8

9

13

Explanation

This question tests solving for an unknown in a simple equation (ISEE Lower Level Mathematics Achievement). Understanding simple equations involves isolating the variable to find its value. In the scenario needing 9 cups of flour with 4 already, solving x + 4 = 9 involves subtracting 4 from both sides. Choice A is correct because it correctly identifies x as 5 when you isolate the variable by subtracting 4 from 9. Choice B is incorrect because it represents the total without solving. To help students: Teach strategies like balancing equations by performing the same operation on both sides. Encourage checking work by substituting values back into the original equation.

3

Mia has ten dollars. She buys a snack for $3$. Solve for $x$: $x + 3 = 10$. What is $x$?

3

7

10

13

Explanation

This question tests solving for an unknown in a simple equation (ISEE Lower Level Mathematics Achievement). Understanding simple equations involves isolating the variable to find its value. In the scenario where Mia has ten dollars and buys a snack for $3, x represents the money left, and solving x + 3 = 10 involves subtracting 3 from both sides. Choice B is correct because it correctly identifies x as 7 when you isolate the variable by subtracting 3 from 10. Choice A is incorrect because it results from misunderstanding the equation as subtraction without isolation. To help students: Teach strategies like balancing equations by performing the same operation on both sides. Encourage checking work by substituting values back into the original equation.

4

After a bird ate 8 berries from a bush, there were 21 berries left. If b represents the original number of berries on the bush, the equation b - 8 = 21 describes the situation. How many berries were on the bush to start?

13

21

29

168

Explanation

The equation b - 8 = 21 shows that the starting number of berries, b, minus the 8 that were eaten, equals 21. To find the starting number, add 8 to the number of berries left: b = 21 + 8, so b = 29. There were 29 berries on the bush.

5

A hike is $15$ miles. Sam walks $5$ miles. What value of $x$ makes $5 + x = 15$ true?

5

10

15

20

Explanation

This question tests solving for an unknown in a simple equation (ISEE Lower Level Mathematics Achievement). Understanding simple equations involves isolating the variable to find its value. In the scenario of a 15-mile hike where Sam walks 5 miles, x represents the remaining distance, and solving 5 + x = 15 involves subtracting 5 from both sides. Choice B is correct because it correctly identifies x as 10 when you isolate the variable by subtracting 5 from 15. Choice A is incorrect because it doubles the total without solving. To help students: Teach strategies like balancing equations by performing the same operation on both sides. Encourage checking work by substituting values back into the original equation.

6

Max has saved $x$ dollars toward $20$. He still needs $5$ dollars. Solve $20 - x = 5$.

5

15

20

25

Explanation

This question tests solving for an unknown in a simple equation (ISEE Lower Level Mathematics Achievement). Understanding simple equations involves isolating the variable to find its value. In the scenario where Max has saved x toward $20 and needs $5, solving 20 - x = 5 involves isolating x to 15. Choice A is correct because it correctly identifies x as 15 when you solve the equation. Choice B is incorrect because it mistakes needed for saved. To help students: Teach strategies like balancing equations by performing the same operation on both sides. Encourage checking work by substituting values back into the original equation.

7

You bike five miles and then $x$ miles. If $5 + x = 15$, what is $x$?

ten

five

twenty

fifteen

Explanation

This question tests solving for an unknown in a simple equation (ISEE Lower Level Mathematics Achievement). Understanding simple equations involves isolating the variable to find its value. In the scenario '5 + x = 15', x represents the unknown number of miles biked after the first five miles, and solving it involves subtracting 5 from both sides. Choice B is correct because it correctly identifies x as 10 when you isolate the variable by subtracting 5 from 15 (15 - 5 = 10). Choice A (twenty) results from adding 5 to 15, Choice C (fifteen) incorrectly uses the total distance, and Choice D (five) simply repeats the known value. To help students: Use visual aids like number lines to show how subtraction helps find the missing part. Practice with real-world contexts to make the concept more concrete and relatable.

8

A bike path is $15$ miles. Kim rides $5$ miles. If $5 + x = 15$, what is $x$?

8

10

15

20

Explanation

This question tests solving for an unknown in a simple equation (ISEE Lower Level Mathematics Achievement). Understanding simple equations involves isolating the variable to find its value. In the scenario of a 15-mile bike path where Kim rides 5 miles, x represents miles left, and solving 5 + x = 15 involves subtracting 5 from both sides. Choice C is correct because it correctly identifies x as 10 when you isolate the variable by subtracting 5 from 15. Choice A is incorrect because it represents the total without solving. To help students: Teach strategies like balancing equations by performing the same operation on both sides. Encourage checking work by substituting values back into the original equation.

9

A baker uses $9$ cups of flour. Four cups are already in the bowl. If $x + 4 = 9$, find $x$.

4

5

9

14

Explanation

This question tests solving for an unknown in a simple equation (ISEE Lower Level Mathematics Achievement). Understanding simple equations involves isolating the variable to find its value. In the scenario where a baker uses 9 cups with 4 already in the bowl, solving x + 4 = 9 involves subtracting 4 from both sides. Choice C is correct because it correctly identifies x as 5 when you isolate the variable by subtracting 4 from 9. Choice A is incorrect because it uses the added amount directly. To help students: Teach strategies like balancing equations by performing the same operation on both sides. Encourage checking work by substituting values back into the original equation.

10

Tia wants $20$ dollars saved. She needs $5$ more. If $20 - x = 5$, find $x$.

5

15

20

25

Explanation

This question tests solving for an unknown in a simple equation (ISEE Lower Level Mathematics Achievement). Understanding simple equations involves isolating the variable to find its value. In the scenario where Tia wants $20 and needs $5 more, solving 20 - x = 5 gives x as saved amount of 15. Choice B is correct because it correctly identifies x as 15 when you isolate the variable. Choice A is incorrect because it uses the needed amount directly. To help students: Teach strategies like balancing equations by performing the same operation on both sides. Encourage checking work by substituting values back into the original equation.

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