Solve 3*(-15/2+1)-2*-15/2+5-35/2=10*-3/2-10+8

$$3 \times (- \frac{ 15 }{ 2 } +1)-2 \times - \frac{ 15 }{ 2 } +5- \frac{ 35 }{ 2 } =10 \times - \frac{ 3 }{ 2 } -10+8$$

Verify

Solution Steps

Convert 1 to fraction \frac{2}{2}.

$$3\left(-\frac{15}{2}+\frac{2}{2}\right)-2\left(-\frac{15}{2}\right)+5-\frac{35}{2}=10\left(-\frac{3}{2}\right)-10+8$$

Since -\frac{15}{2} and \frac{2}{2} have the same denominator, add them by adding their numerators.

$$3\times \frac{-15+2}{2}-2\left(-\frac{15}{2}\right)+5-\frac{35}{2}=10\left(-\frac{3}{2}\right)-10+8$$

Add -15 and 2 to get -13.

$$3\left(-\frac{13}{2}\right)-2\left(-\frac{15}{2}\right)+5-\frac{35}{2}=10\left(-\frac{3}{2}\right)-10+8$$

Express 3\left(-\frac{13}{2}\right) as a single fraction.

$$\frac{3\left(-13\right)}{2}-2\left(-\frac{15}{2}\right)+5-\frac{35}{2}=10\left(-\frac{3}{2}\right)-10+8$$

Multiply 3 and -13 to get -39.

$$\frac{-39}{2}-2\left(-\frac{15}{2}\right)+5-\frac{35}{2}=10\left(-\frac{3}{2}\right)-10+8$$

Fraction \frac{-39}{2} can be rewritten as -\frac{39}{2} by extracting the negative sign.

$$-\frac{39}{2}-2\left(-\frac{15}{2}\right)+5-\frac{35}{2}=10\left(-\frac{3}{2}\right)-10+8$$

Cancel out 2 and 2.

$$-\frac{39}{2}-\left(-15\right)+5-\frac{35}{2}=10\left(-\frac{3}{2}\right)-10+8$$

The opposite of -15 is 15.

$$-\frac{39}{2}+15+5-\frac{35}{2}=10\left(-\frac{3}{2}\right)-10+8$$

Convert 15 to fraction \frac{30}{2}.

$$-\frac{39}{2}+\frac{30}{2}+5-\frac{35}{2}=10\left(-\frac{3}{2}\right)-10+8$$

Since -\frac{39}{2} and \frac{30}{2} have the same denominator, add them by adding their numerators.

$$\frac{-39+30}{2}+5-\frac{35}{2}=10\left(-\frac{3}{2}\right)-10+8$$

Add -39 and 30 to get -9.

$$-\frac{9}{2}+5-\frac{35}{2}=10\left(-\frac{3}{2}\right)-10+8$$

Convert 5 to fraction \frac{10}{2}.

$$-\frac{9}{2}+\frac{10}{2}-\frac{35}{2}=10\left(-\frac{3}{2}\right)-10+8$$

Since -\frac{9}{2} and \frac{10}{2} have the same denominator, add them by adding their numerators.

$$\frac{-9+10}{2}-\frac{35}{2}=10\left(-\frac{3}{2}\right)-10+8$$

Add -9 and 10 to get 1.

$$\frac{1}{2}-\frac{35}{2}=10\left(-\frac{3}{2}\right)-10+8$$

Since \frac{1}{2} and \frac{35}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1-35}{2}=10\left(-\frac{3}{2}\right)-10+8$$

Subtract 35 from 1 to get -34.

$$\frac{-34}{2}=10\left(-\frac{3}{2}\right)-10+8$$

Divide -34 by 2 to get -17.

$$-17=10\left(-\frac{3}{2}\right)-10+8$$

Express 10\left(-\frac{3}{2}\right) as a single fraction.

$$-17=\frac{10\left(-3\right)}{2}-10+8$$

Multiply 10 and -3 to get -30.

$$-17=\frac{-30}{2}-10+8$$

Divide -30 by 2 to get -15.

$$-17=-15-10+8$$

Subtract 10 from -15 to get -25.

$$-17=-25+8$$

Add -25 and 8 to get -17.

$$-17=-17$$

Compare -17 and -17.

$$\text{true}$$