Pre-Algebra Examples

$9 t - 21 = 3 (t - 7) + 6 t$

Step 1

Since $t$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$3 (t - 7) + 6 t = 9 t - 21$

Step 2

Simplify $3 (t - 7) + 6 t$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$3 t + 3 \cdot - 7 + 6 t = 9 t - 21$

Step 2.1.2

Multiply $3$ by $- 7$ .

$3 t - 21 + 6 t = 9 t - 21$

Step 2.2

Add $3 t$ and $6 t$ .

$9 t - 21 = 9 t - 21$

Step 3

Move all terms containing $t$ to the left side of the equation.

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Step 3.1

Subtract $9 t$ from both sides of the equation.

$9 t - 21 - 9 t = - 21$

Step 3.2

Combine the opposite terms in $9 t - 21 - 9 t$ .

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Step 3.2.1

Subtract $9 t$ from $9 t$ .

$0 - 21 = - 21$

Step 3.2.2

Subtract $21$ from $0$ .

$- 21 = - 21$

Step 4

Since $- 21 = - 21$ , the equation will always be true for any value of $t$ .

All real numbers

Step 5

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$