Algebra Examples

$h (x) = (3 x - 19) - (- 18 + 5 x)$

Step 1

Write $h (x) = (3 x - 19) - (- 18 + 5 x)$ as an equation.

$y = (3 x - 19) - (- 18 + 5 x)$

Step 2

Solve the equation for $y$ .

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Step 2.1

Remove parentheses.

$y = 3 x - 19 - (- 18 + 5 x)$

Step 2.2

Simplify $3 x - 19 - (- 18 + 5 x)$ .

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Step 2.2.1

Simplify each term.

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Step 2.2.1.1

Apply the distributive property.

$y = 3 x - 19 - - 18 - (5 x)$

Step 2.2.1.2

Multiply $- 1$ by $- 18$ .

$y = 3 x - 19 + 18 - (5 x)$

Step 2.2.1.3

Multiply $5$ by $- 1$ .

$y = 3 x - 19 + 18 - 5 x$

Step 2.2.2

Simplify by adding terms.

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Step 2.2.2.1

Subtract $5 x$ from $3 x$ .

$y = - 2 x - 19 + 18$

Step 2.2.2.2

Add $- 19$ and $18$ .

$y = - 2 x - 1$

Step 3

Choose any value for $x$ that is in the domain to plug into the equation.

Step 4

Choose $0$ to substitute in for $x$ to find the ordered pair.

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Step 4.1

Remove parentheses.

$y = - 2 \cdot 0 - 1$

Step 4.2

Simplify $- 2 \cdot 0 - 1$ .

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Step 4.2.1

Multiply $- 2$ by $0$ .

$y = 0 - 1$

Step 4.2.2

Subtract $1$ from $0$ .

$y = - 1$

Step 4.3

Use the $x$ and $y$ values to form the ordered pair.

$(0, - 1)$

Step 5

Choose $1$ to substitute in for $x$ to find the ordered pair.

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Step 5.1

Remove parentheses.

$y = - 2 \cdot 1 - 1$

Step 5.2

Simplify $- 2 \cdot 1 - 1$ .

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Step 5.2.1

Multiply $- 2$ by $1$ .

$y = - 2 - 1$

Step 5.2.2

Subtract $1$ from $- 2$ .

$y = - 3$

Step 5.3

Use the $x$ and $y$ values to form the ordered pair.

$(1, - 3)$

Step 6

Choose $2$ to substitute in for $x$ to find the ordered pair.

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Step 6.1

Remove parentheses.

$y = - 2 \cdot 2 - 1$

Step 6.2

Simplify $- 2 \cdot 2 - 1$ .

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Step 6.2.1

Multiply $- 2$ by $2$ .

$y = - 4 - 1$

Step 6.2.2

Subtract $1$ from $- 4$ .

$y = - 5$

Step 6.3

Use the $x$ and $y$ values to form the ordered pair.

$(2, - 5)$

Step 7

These are three possible solutions to the equation.

$(0, - 1), (1, - 3), (2, - 5)$

Step 8