Solve {l}{(a+3)*(-3/4)=(a-2)*3=-3}{3a-9-3a-6=-3}

$$\left. \begin{array} { l } { ( a + 3 ) \cdot ( - \frac { 3 } { 4 } ) = ( a - 2 ) \cdot 3 = - 3 } \\ { 3 a - 9 - 3 a - 6 = - 3 } \end{array} \right.$$

Solve for a

$$a=1$$

Steps for Solving Linear Equation

Use the distributive property to multiply a+3 by -\frac{3}{4}.

$$a\left(-\frac{3}{4}\right)+3\left(-\frac{3}{4}\right)=\left(a-2\right)\times 3$$

Express 3\left(-\frac{3}{4}\right) as a single fraction.

$$a\left(-\frac{3}{4}\right)+\frac{3\left(-3\right)}{4}=\left(a-2\right)\times 3$$

Multiply 3 and -3 to get -9.

$$a\left(-\frac{3}{4}\right)+\frac{-9}{4}=\left(a-2\right)\times 3$$

Fraction \frac{-9}{4} can be rewritten as -\frac{9}{4} by extracting the negative sign.

$$a\left(-\frac{3}{4}\right)-\frac{9}{4}=\left(a-2\right)\times 3$$

Use the distributive property to multiply a-2 by 3.

$$a\left(-\frac{3}{4}\right)-\frac{9}{4}=3a-6$$

Subtract 3a from both sides.

$$a\left(-\frac{3}{4}\right)-\frac{9}{4}-3a=-6$$

Combine a\left(-\frac{3}{4}\right) and -3a to get -\frac{15}{4}a.

$$-\frac{15}{4}a-\frac{9}{4}=-6$$

Add \frac{9}{4} to both sides.

$$-\frac{15}{4}a=-6+\frac{9}{4}$$

Convert -6 to fraction -\frac{24}{4}.

$$-\frac{15}{4}a=-\frac{24}{4}+\frac{9}{4}$$

Since -\frac{24}{4} and \frac{9}{4} have the same denominator, add them by adding their numerators.

$$-\frac{15}{4}a=\frac{-24+9}{4}$$

Add -24 and 9 to get -15.

$$-\frac{15}{4}a=-\frac{15}{4}$$

Multiply both sides by -\frac{4}{15}, the reciprocal of -\frac{15}{4}.

$$a=-\frac{15}{4}\left(-\frac{4}{15}\right)$$

Multiply -\frac{15}{4} times -\frac{4}{15} by multiplying numerator times numerator and denominator times denominator.

$$a=\frac{-15\left(-4\right)}{4\times 15}$$

Do the multiplications in the fraction \frac{-15\left(-4\right)}{4\times 15}.

$$a=\frac{60}{60}$$

Divide 60 by 60 to get 1.

$$a=1$$