Q: A chemist mixes $$x$$ liters of a $$10\%$$ acid solution with $$5$$ liters of a $$20\%$$ acid solution to obtain a $$15\%$$ acid solution. Which equation models this scenario?

$$0.10x + 0.20 \times 5 = 0.15(x + 5)$$

Question 1

Solve for $$x in $$the equation $$2x + 5 = 9.$$

Accepted Answer

$$x = 2$$

Question 2

A restaurant bill is $$48$$ before tax. You have a coupon for $$x$$ dollars off. After using the coupon and adding $$8\%$$ tax, the total is $$46.44. $$Which equation represents this situation?

Accepted Answer

$$1.08(48 - x) = 46.44$$

Question 3

Which of the following is the correct first step to solve $$\frac{1}{3}x - \frac{1}{4}x = 16$$?

Accepted Answer

Multiply both sides by $$12 to $$clear fractions.

Question 4

Simplify and solve: $$-4x - 1 + 5x = 9x + 3 - 7x.$$

Accepted Answer

$$x = 2$$

Question 5

Which property of equality justifies the step from $$2x + 5 = 9 to$$ $$2x = 4$$?

Accepted Answer

Subtraction property of equality

Question 6

Solve for $$c in$$ $$0.6 = 2 - 3.5c.$$

Accepted Answer

$$c = 0.4$$

Question 7

Which equation is an identity (true for all real numbers)?

Accepted Answer

$$2(x + 1) = 2x + 2$$

Question 8

What is the solution to $$2(x - 3) = 5x - 9$$?

Accepted Answer

$$x = 1$$

Question 9

Which of the following equations is a contradiction (has no solution)?

Accepted Answer

$$2x + 3 = 2x + 5$$

Question 10

A chemist mixes $$x$$ liters of a $$10\%$$ acid solution with $$5$$ liters of a $$20\%$$ acid solution to obtain a $$15\%$$ acid solution. Which equation models this scenario?

Accepted Answer

$$0.10x + 0.20 	imes 5 = 0.15(x + 5)$$

Question 11

Solve for $$x$$: $$x + 52 + 12 = 2x - x - 38.$$

Accepted Answer

$$x = -102$$

Question 12

Which of the following best describes the equation $$3x + 5 = 3(x + 2)$$?

Accepted Answer

Contradiction

Question 13

A student solves $$3x - 5 = 16$$ and writes $$3x = 11$$, then $$3x3 = 113$$, then $$x = 113. $$What was the main error?

Accepted Answer

Incorrectly multiplied both sides by $$3$$ instead of dividing by $$3.$$

Question 14

Solve for $$x$$: $$0.3x + 0.1 = 0.27x - 0.02.$$

Accepted Answer

$$x = 0.4$$

Question 15

Which step should be performed first when solving $$2(x - 3) = 5x - 9$$?

Accepted Answer

Apply the distributive property to remove parentheses.

Question 16

If you solve $$4n - 9n + 6 = 0$$, what is the value of $$n$$?

Accepted Answer

$$n = -1.2$$

Question 17

Which of the following is NOT a valid step when solving a linear equation with fractions?

Accepted Answer

Divide both sides by zero.

Question 18

If $$z = -2$$, what is the solution to the equation $$z = -2$$?

Accepted Answer

$$z = -2$$

Question 19

Which of the following best describes the equation $$x + 2 = x + 2$$?

Accepted Answer

Identity

Solving Linear Equations in One Variable

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