Solve (x+3)/(7)-1=(2x+5)/(3)-2 | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$\frac{ x+3 }{ 7 } -1= \frac{ 2x+5 }{ 3 } -2$$

Solve for x

$x=-\frac{5}{11}\approx -0.454545455$

Steps for Solving Linear Equation

Multiply both sides of the equation by $21$, the least common multiple of $7,3$.

$$3\left(x+3\right)-21=7\left(2x+5\right)-42$$

Use the distributive property to multiply $3$ by $x+3$.

$$3x+9-21=7\left(2x+5\right)-42$$

Subtract $21$ from $9$ to get $-12$.

$$3x-12=7\left(2x+5\right)-42$$

Use the distributive property to multiply $7$ by $2x+5$.

$$3x-12=14x+35-42$$

Subtract $42$ from $35$ to get $-7$.

$$3x-12=14x-7$$

Subtract $14x$ from both sides.

$$3x-12-14x=-7$$

Combine $3x$ and $-14x$ to get $-11x$.

$$-11x-12=-7$$

Add $12$ to both sides.

$$-11x=-7+12$$

Add $-7$ and $12$ to get $5$.

$$-11x=5$$

Divide both sides by $-11$.

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

Fraction $\frac{5}{-11}$ can be rewritten as $-\frac{5}{11}$ by extracting the negative sign.

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