Linear equations in one variable — Topic practice

5 exercises · 5 automatically checked · Untimed

Instructions and review guidance

5 questions · Shuffled order · Untimed practice

Work through the set before checking solutions. Guide question labels match the source lesson references.

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Question 1

Guide question E1A

5 − 2(3x − 4) = 25. Find x.

Your answer

Enter an integer, decimal or fraction without units. Use up to 5 characters, or 6 including a leading minus.

Why this answer

$x = -2$ . Distribute the negative factor: $5 - 6x + 8 = 25,$ so $-6x = 12$ and $x = -2.$ Check: $5 - 2(-10) = 25.$

Review lesson: Linear equations in one variable

Question 2

Guide question E1B

(x + 1)/2 − (x − 2)/3 = 4. Find x.

Your answer

Enter an integer, decimal or fraction without units. Use up to 5 characters, or 6 including a leading minus.

Why this answer

$x = 17$ . Multiply the whole equation by 6: $3(x + 1) - 2(x - 2) = 24.$ Then $3x + 3 - 2x + 4 = 24,$ so $x + 7 = 24$ and $x = 17.$

Review lesson: Linear equations in one variable

Question 3

Guide question E1C

7(2x + 3) = 63. Find 4x + 6.

Your answer

Enter an integer, decimal or fraction without units. Use up to 5 characters, or 6 including a leading minus.

Why this answer

18. Divide by 7 to get $2x + 3 = 9.$ The requested expression is $4x + 6 = 2(2x + 3) = 18.$ Solving for x is optional.

Review lesson: Linear equations in one variable

Question 4

Guide question E1D

For which k does k(x + 2) = 5x + 1 have no solution?

Your answer

Enter an integer, decimal or fraction without units. Use up to 5 characters, or 6 including a leading minus.

Why this answer

$k = 5$ . Expanding gives $kx + 2k = 5x + 1.$ At $k = 5$ the variable terms cancel but the constants disagree: $10 = 1.$ For any other k, the nonzero variable coefficient gives a unique solution.

Review lesson: Linear equations in one variable

Question 5

Guide question E1E

a(x + 3) + b = 4x − 2 for every real x. Find a + b.

Your answer

Enter an integer, decimal or fraction without units. Use up to 5 characters, or 6 including a leading minus.

Why this answer

−10. Match coefficients in $ax + 3a + b = 4x - 2.$ Then $a = 4$ and $12 + b = -2,$ so $b = -14$ and $a + b = -10.$

Review lesson: Linear equations in one variable

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