How to solve two-step equations

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Algebra › How to solve two-step equations

Questions 1 - 10

Solve for :

$\frac{1}{2} x - 4 = \frac{3}{10}x + \frac{2}{5}$

$x=\frac{11}{5}$

$x=\frac{22}{5}$

$x=\frac{44}{5}$

Explanation

$\frac{1}{2} x - 4 = \frac{3}{10}x + \frac{2}{5}$

$10 \cdot \left (\frac{1}{2} x - 4 \right )=10 \cdot \left ( \frac{3}{10}x + \frac{2}{ 5} \right )$

$\frac{10}{1} \cdot \frac{1}{2} x - \frac{10}{1} \cdot \frac{4}{1} \right )=\frac{10}{1} \cdot \frac{3}{10}x +\frac{10}{1} \cdot \frac{2}{ 5}$

$\frac{5}{1} \cdot \frac{1}{1} x - \frac{10}{1} \cdot \frac{4}{1} \right )=\frac{1}{1} \cdot \frac{3}{1}x +\frac{2}{1} \cdot \frac{2}{ 1}$

What order of operations would result in solving the equation for ?

Taking the root, then subtraction, then division

Cubing, then division, then addition

Taking the root, then division, then addition

Division, then taking the root, then subtraction

Multiplication, then taking the root, then subtraction

Explanation

Take the root.

Subtract from both sides.

$s = -\frac{1}{2}$ Divide both sides by and simplify.

Solve for .

Explanation

Add 5 to each side of the equation.

Add 3x to each side of the equation.

Divide each side of the equation by 5.

Solve for the unknown variable.

$\frac{4}{3}$

$-\frac{4}{3}$

$\frac{3}{4}$

Explanation

Add four on both sides to isolate the term.

Simplify both sides.

Divide by negative three on both sides.

$\frac{-3x}{-3}=\frac{-4}{-3}$

A negative number divided by a negative number will be a positive number.

$x=\frac{4}{3}$

Evaluate $(x+3)^2-\frac{18}{2}$ when x = 3.

–3

Explanation

First plug 3 in for x, giving you $(6)^2-\frac{18}{2}$ . You square 6, giving you 36, then subtract (18/2), giving you 27.

$(x+3)^2-\frac{18}{2}$

$(3+3)^2-\frac{18}{2}$

Solve the equation:

$\frac{7}{3}$

$-\frac{7}{3}$

$\frac{14}{6}$

$\frac{12}{5}$

$-\frac{14}{6}$

Explanation

Add four on both sides to bring the four to the right side of the equation.

Simplify both sides.

Divide both sides by six.

$x=\frac{14}{6}$

This fraction is not reduced. Reduce the fraction by writing out the factors.

$x=\frac{14}{6} =\frac{2\times 7}{2 \times 3}$

Cancel out or divide the twos.

The answer is: $\frac{7}{3}$

The price for renting a cement truck has two parts. The renter must first pay a flat price of \$175 for using the truck. On top of that, every hour that the truck is away from the shop adds twenty dollars to the bill. Write an equation to express the total price of using the truck for number of hours.

Explanation

First, define your variables:

number of hours the truck is in use

total price

Even though the question gives the definitions, it's always helpful to rewrite them.

A flat price is the part of the price that is dependent on nothing. So the flat price stands alone:

The amount of money that the \$20 rate will demand from the renter is dependent on the number of hours the truck is in use, as it is a rate and therefore involves some sort of time. Thus it is clear from looking at the definition of our variables that the 20 must be multiplied by to determine how much more the renter must pay for the truck's use, on top of the \$175. The two numbers must be added together to find the final price, which includes both.

Solve for :

$\frac{34}{3}$

Explanation

$\frac{3x}{3}=\frac{24}{3}$

Solve the following equation for :

Explanation

This equation takes two steps to solve. When solving two steps, first we simplify the addition and subtraction terms. Then we do the multiplication/division step.

So, in , our first step is to negate the subtraction of 13. The inverse of subtracting by 13 is to add by 13. So step 1 is to add 13 to both sides. We have

From here, we do a second step to solve for , by doing the inverse of multiplying by 2. The inverse of multiplication is division. So to "get rid" of the 2, we divide both sides by 2. So from,