Algebra Examples

$3 (2 x + 1) - x = 5 x + 3$

Step 1

Simplify $3 (2 x + 1) - x$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$3 (2 x) + 3 \cdot 1 - x = 5 x + 3$

Step 1.1.2

Multiply $2$ by $3$ .

$6 x + 3 \cdot 1 - x = 5 x + 3$

Step 1.1.3

Multiply $3$ by $1$ .

$6 x + 3 - x = 5 x + 3$

Step 1.2

Subtract $x$ from $6 x$ .

$5 x + 3 = 5 x + 3$

Step 2

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

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Step 2.1

Subtract $5 x$ from both sides of the equation.

$5 x + 3 - 5 x = 3$

Step 2.2

Combine the opposite terms in $5 x + 3 - 5 x$ .

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Step 2.2.1

Subtract $5 x$ from $5 x$ .

$0 + 3 = 3$

Step 2.2.2

Add $0$ and $3$ .

$3 = 3$

Step 3

Since $3 = 3$ , the equation will always be true for any value of $x$ .

All real numbers

Step 4

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$