Algebra I (MAT111): Solving One-Step Equations (practice)

Guidance

When solving an equation for a variable, you must get the variable by itself. All the equations in this practice quiz are linear equations. That means the equation can be simplified to $ax+b=c$ , where $a, b$ , and $c$ are real numbers. Here we will only deal with using one operation; addition, subtraction, multiplication or division.

Bismarck Standards this activity aligns:

MAT-HS.A-REI.01 Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.
MAT-HS.A-REI.03 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
MAT-HS.A-REI.04 Solve quadratic equations in one variable

Example A

Solve $7+y=16$ for $y$ .

Solution: This problem is simple and you could probably solve it in your head. However, to start good practices, you should always use algebra to solve any equation. Even if the problem seems easy, equations will get more difficult to solve.

To solve an equation for a variable, you must do the opposite, or undo, whatever is on the same side as the variable. 7 is being added to $y$ , so we must subtract 7 from both sides. Notice that this is very similar to the previous concept ( Solving Algebraic Equations for a Variable ).

$& \ \bcancel{7}+y = 16\\& \underline{-\bcancel{7} \quad \quad -7 \; \;}\\& \ \quad \ \ y = 9$

You can check that $y= 9$ is correct by plugging 9 back into the original equation. 7 + 9 does equal 16, so we know that we found the correct answer.

Example B

Solve $-7h=84$ .

Solution: Recall that $-7h = -7 \times h$ , so the opposite, or inverse , operation of multiplication is division. Therefore, we must divide both sides by -7 to solve for $h$ .

$\frac{-\bcancel{7}h}{-\bcancel{7}} &= \frac{84}{-7}\\h &= -12$

Again, check your work. $-7 \cdot -12$ is equal to 84, so we know our answer is correct.

Example C

Solve $\frac{3}{8} x = \frac{3}{2}$ .

Solution: The variable is being multiplied by a fraction. Instead of dividing by a fraction, we multiply by the reciprocal of $\frac{3}{8}$ , which is $\frac{8}{3}$ .

$\xcancel{\frac{8}{3} \cdot \frac{3}{8}} x &= \bcancel{\frac{3}{2} \cdot \frac{8}{3}}\\x &= \frac{8}{2}=4$

Check the answer: $\frac{3}{_2\cancel{8}} \cdot \cancel{4}=\frac{3}{2}$ . This is correct, so we know that $x = 4$ is the answer.

Instructions:

Work the problems out on paper before entering answers into Moodle. Bring your work to school because we will discuss your work. This Moodle practice quiz will provide feedback on how to solve the problems. So you are allows to retake as many times as necessary for you understand the one-step equations. (note the questions will change)

Grading method: Highest grade