Option C x equals nineteen twelfths \( (x=\frac{19}{12} \) and y equals sixteen thirds \( y=\frac{16}{3}) \) should be selected.
Here's a possible strategy for solving the first equation:One half open parenthesis x minus three fourths close parenthesis equals five twelfths. Second equation, three fourths y minus three halves equals five halves.
$$ \frac{1}{2} \left( x - \frac{3}{4} \right) = \frac{5}{12} $$
1. Distribute the one half \( \frac{1}{2} \) on the left side, and then perform the multiplication.one half times x minus one half times three fourths equals five twelfths
$$ \frac{1}{2} \cdot x \, - \, \frac{1}{2} \cdot \frac{3}{4} \, = \, \frac{5}{12} $$
fraction with numerator of x and denominator of 2 minus 3 eighths equals 5 twelfths $$ \frac{x}{2} - \frac{3}{8} = \frac{5}{12} $$
2. Isolate the term with x by adding three eighths \( \frac{3}{8} \) to both sides of the equation.fraction with numerator of x and denominator of 2 minus 3 eighths plus 3 eighths equals five twelfths plus 3 eighths
$$ \frac{x}{2} - \frac{3}{8} + \frac{3}{8} = \frac{5}{12} + \frac{3}{8} $$
fraction with numerator of x and denominator of 2 equals 10 twenty fourths plus 9 twenty fourths $$ \frac{x}{2} = \frac{10}{24} + \frac{9}{24} $$
fraction with numerator of x and denominator of 2 equals 19 twenty fourths $$ \frac{x}{2} = \frac{19}{24} $$
3. Multiply both sides of the equation by 2 to isolate the variable (multiply out the 2 that is dividing the x on the left side):fraction with numerator of x and denominator of 2 times 2 equals 19 twenty fourths times 2
$$ \frac{x}{2} \cdot 2 = \frac{19}{24} \cdot 2 $$
x equals 38 twenty fourths, which equals 19 twelfths $$ x = \frac{38}{24} = \frac{19}{12} $$
Here's a possible strategy for solving the second equation:Three fourths y minus three halves equals five halves.
$$ \frac{3}{4} y - \frac{3}{2} = \frac{5}{2} $$
1. Isolate the term with y by adding three halves \( \frac{3}{2} \) to both sides. Perform the addition.3 fourths y minus 3 halves plus 3 halves equals 5 halves plus 3 halves
$$ \frac{3}{4}y - \frac{3}{2} + \frac{3}{2} = \frac{5}{2} + \frac{3}{2} $$
three fourths Y equals 8 halves $$ \frac{3}{4}y = \frac{8}{2} $$
three fourths Y equals 4 $$ \frac{3}{4}y = 4 $$
2. Multiply both sides by four thirds \( \frac{4}{3} \) to solve for y:four thirds times three fourths y equals 4 times four thirds
$$ \frac{4}{3} \cdot \frac{3}{4}y = 4 \cdot \frac{4}{3} $$
y equals 16 thirds $$ y=\frac{16}{3} $$
