Solve x=[59/17-(-5.375)]-[(-35/8)-(+18/17)]

$$x = [ 5 \frac { 9 } { 17 } - ( - 5.375 ) ] - [ ( - 3 \frac { 5 } { 8 } ) - ( + 1 \frac { 8 } { 17 } ) ]$$

Solve for x

$$x=16$$

Steps for Solving Linear Equation

Multiply 5 and 17 to get 85.

$$x=\frac{85+9}{17}-\left(-5.375\right)-\left(-\frac{3\times 8+5}{8}-\frac{1\times 17+8}{17}\right)$$

Add 85 and 9 to get 94.

$$x=\frac{94}{17}-\left(-5.375\right)-\left(-\frac{3\times 8+5}{8}-\frac{1\times 17+8}{17}\right)$$

The opposite of -5.375 is 5.375.

$$x=\frac{94}{17}+5.375-\left(-\frac{3\times 8+5}{8}-\frac{1\times 17+8}{17}\right)$$

Convert decimal number 5.375 to fraction \frac{5375}{1000}. Reduce the fraction \frac{5375}{1000} to lowest terms by extracting and canceling out 125.

$$x=\frac{94}{17}+\frac{43}{8}-\left(-\frac{3\times 8+5}{8}-\frac{1\times 17+8}{17}\right)$$

Least common multiple of 17 and 8 is 136. Convert \frac{94}{17} and \frac{43}{8} to fractions with denominator 136.

$$x=\frac{752}{136}+\frac{731}{136}-\left(-\frac{3\times 8+5}{8}-\frac{1\times 17+8}{17}\right)$$

Since \frac{752}{136} and \frac{731}{136} have the same denominator, add them by adding their numerators.

$$x=\frac{752+731}{136}-\left(-\frac{3\times 8+5}{8}-\frac{1\times 17+8}{17}\right)$$

Add 752 and 731 to get 1483.

$$x=\frac{1483}{136}-\left(-\frac{3\times 8+5}{8}-\frac{1\times 17+8}{17}\right)$$

Multiply 3 and 8 to get 24.

$$x=\frac{1483}{136}-\left(-\frac{24+5}{8}-\frac{1\times 17+8}{17}\right)$$

Add 24 and 5 to get 29.

$$x=\frac{1483}{136}-\left(-\frac{29}{8}-\frac{1\times 17+8}{17}\right)$$

Multiply 1 and 17 to get 17.

$$x=\frac{1483}{136}-\left(-\frac{29}{8}-\frac{17+8}{17}\right)$$

Add 17 and 8 to get 25.

$$x=\frac{1483}{136}-\left(-\frac{29}{8}-\frac{25}{17}\right)$$

Least common multiple of 8 and 17 is 136. Convert -\frac{29}{8} and \frac{25}{17} to fractions with denominator 136.

$$x=\frac{1483}{136}-\left(-\frac{493}{136}-\frac{200}{136}\right)$$

Since -\frac{493}{136} and \frac{200}{136} have the same denominator, subtract them by subtracting their numerators.

$$x=\frac{1483}{136}-\frac{-493-200}{136}$$

Subtract 200 from -493 to get -693.

$$x=\frac{1483}{136}-\left(-\frac{693}{136}\right)$$

The opposite of -\frac{693}{136} is \frac{693}{136}.

$$x=\frac{1483}{136}+\frac{693}{136}$$

Since \frac{1483}{136} and \frac{693}{136} have the same denominator, add them by adding their numerators.

$$x=\frac{1483+693}{136}$$

Add 1483 and 693 to get 2176.

$$x=\frac{2176}{136}$$

Divide 2176 by 136 to get 16.

$$x=16$$

Assign x

$$x≔16$$