Step 1: Find the LCD of all fractions in the equation.

The LCD is [latex]8[/latex].

Step 2: Multiply both sides by the LCD.

[latex]{\color{red}{8}}{\left(a+\frac34\right)=}{\color{red}{8}}{\left(\frac38a-\frac12\right)}[/latex]

Step 3: Distribute.

[latex]\begin{align*}&\;&8\cdot a+8\cdot\frac34&=8\cdot\frac38a-8\cdot\frac12\\ &\text{Simplify -  no more fractions.}\;&8a+6&=3a-4\end{align*}[/latex]

Step 4: Subtract [latex]3a[/latex] from both sides.

[latex]\begin{align*}&\;&8a{\color{red}{-}}{\color{red}{3}}{\color{red}{a}}+6&=3a{\color{red}{-}}{\color{red}{3}}{\color{red}{a}}-4\\ &\text{Simplify.}\;&5a+6&=-4 \end{align*}[/latex]

Step 5: Subtract [latex]6[/latex] from both sides.

[latex]\begin{align*}&\;&5a+6{\color{red}{-}}{\color{red}{6}}&=-4{\color{red}{-}}{\color{red}{6}}\\ &\text{Simplify.}\;&5a&=-10 \end{align*}[/latex]

Step 6: Divide by [latex]5[/latex].

[latex]\begin{align*}&\;&\frac{5a}{\color{red}{5}}&=\frac{-10}{\color{red}{5}}\\ &\text{Simplify.}\;&a&=-2 \end{align*}[/latex]

Step 7: Check:

[latex]a+\frac34=\frac38a-\frac12[/latex]

Step 8: Let [latex]a=-2[/latex].

[latex]\begin{align*} {\color{red}{-}}{\color{red}{2}}+\frac34&\overset?=\frac38\left({\color{red}{-}}{\color{red}{2}}\right)-\frac12\\ -\frac84+\frac34&\overset?=-\frac{16}8-\frac48\\ -\frac54&=-\frac{10}8\\ -\frac54&=-\frac54\checkmark \end{align*}[/latex]

Step 1: Distribute.

[latex]\begin{align*}&\;&-5&=\frac14\cdot8x+\frac14\cdot4\\ &\text{Simplify.}\;&-5&=2x+1 \end{align*}[/latex]

Now there are no fractions.

Step 2: Subtract [latex]1[/latex] from both sides.

[latex]\begin{align*}&\;&-5{\color{red}{-}}{\color{red}{1}}&=2+1{\color{red}{-}}{\color{red}{1}}\\ &\text{Simplify.}\;&-6&=2x \end{align*}[/latex]

Step 3: Divide by [latex]2[/latex].

[latex]\begin{align*}&\;&\frac{-6}{\color{red}{2}}&=\frac{2x}{\color{red}{2}}\\ &\text{Simplify.}\;&-3&=x \end{align*}[/latex]

Step 4: Check:

[latex]-5=\frac14(8x+4)[/latex]

Step 5: Let [latex]x=-3[/latex].

[latex]\begin{align*} -5&\overset?=\frac12\left(4\left({\color{red}{-}}{\color{red}{3}}\right)+2\right)\\ -5&\overset?=\frac12\left(-12+2\right)\\ -5&\overset?=\frac12\left(-10\right)\\ -5&=-5\checkmark \end{align*}[/latex]

Step 1: Distribute.

[latex]\begin{align*}&\;&\frac12\cdot y-\frac12\cdot5&=\frac14\cdot y-\frac14\cdot1\\ &\text{Simplify.}\;&\frac12y-\frac52&=\frac14y-\frac14 \end{align*}[/latex]

Step 2: Multiply by the LCD, [latex]4[/latex].

[latex]\begin{align*}&\;&{\color{red}{4}}\left(\frac12y-\frac52\right)&={\color{red}{4}}\left(\frac14y-\frac14\right)\\ &\text{Distribute.}\;&4\cdot\frac12y-4\cdot\frac52&=4\cdot\frac14y-4\cdot\frac14\\ &\text{Simplify.}\;&2y-10&=y-1 \end{align*}[/latex]

Step 3: Collect the variables to the left.

[latex]\begin{align*}&\;&2y{\color{red}{-}}{\color{red}{y}}-10&=y{\color{red}{-}}{\color{red}{y}}-1\\ &\text{Simplify.}\;&y-10&=-1 \end{align*}[/latex]

Step 4: Collect the constants to the right.

[latex]\begin{align*}&\;&y-10{\color{red}{+}}{\color{red}{10}}&=-1{\color{red}{+}}{\color{red}{10}}\\ &\text{Simplify.}\;&y&=9 \end{align*}[/latex]

Step 5: Check:

[latex]\frac12(y-5)=\frac14(y-1)[/latex]

Step 6: Let [latex]y=9[/latex].

[latex]\frac12\left({\color{red}{9}}-5\right)\overset?=\frac14\left({\color{red}{9}}-1\right)[/latex]

Finish the check on your own.

Look at the decimals and think of the equivalent fractions.

[latex]0.06=\frac{6}{100}[/latex]        [latex] 0.02=\frac{2}{100}[/latex]        [latex]0.25=\frac{25}{100}[/latex]          [latex]1.5=1\frac{5}{10}[/latex]

Notice, that the LCD is [latex]100[/latex].
By multiplying by the LCD, we will clear the decimals from the equation.

[latex]0.06x+0.02=0.25x-1.5[/latex]

Step 1: Multiply both sides by [latex]100[/latex].

[latex]{\color{red}{100}}{(0.06x+0.02)=}{\color{red}{100}}{(0.25x-1.5)}[/latex]

Step 2: Distribute.

[latex]100(0.06x)+100(0.02)=100(0.25x)-100(1.5)[/latex]

Step 3: Multiply, and now we have no more decimals.

[latex]6x+2=25x-150[/latex]

Step 4: Collect the variables to the right.

[latex]\begin{align*}&\;&6x{\color{red}{-}}{\color{red}{6}}{\color{red}{x}}+2&=25x{\color{red}{-}}{\color{red}{6}}{\color{red}{x}}-150\\ &\text{Simplify.}\;&2&=19x-150\\ \end{align*}[/latex]

Step 5: Collect the constants to the left.

[latex]\begin{align*}&\;&2{\color{red}{+}}{\color{red}{150}}&=19x-150{\color{red}{+}}{\color{red}{150}}\\ &\text{Simplify.}\;&152&=19x\\ \end{align*}[/latex]

Step 6: Divide by [latex]19[/latex].

[latex]\begin{align*}&\;&\frac{152}{\color{red}{19}}&=\frac{19x}{\color{red}{19}}\\ &\text{Simplify.}\;&8&=x\\ \end{align*}[/latex]

Step 7: Check: Let [latex]x=8[/latex].

[latex]\begin{align*} 0.06\left({\color{red}{8}}\right)+0.02&\overset?=0.25\left({\color{red}{8}}\right)-1.5\\ 0.48+0.02&\overset?=2.00-1.5\\ 0.50&=0.50\checkmark \end{align*}[/latex]

Step 1: Distribute first.

[latex]0.25x+0.05x+0.15=2.85[/latex]

Step 2: Combine like terms.

[latex]0.30x+0.15=2.85[/latex]

Step 3: To clear decimals, multiply by [latex]100[/latex].

[latex]{\color{red}{100}}{\left(0.30x+0.15\right)=}{\color{red}{100}}{\left(2.8\right)}[/latex]

Step 4: Distribute.

[latex]30x+15=285[/latex]

Step 5: Subtract [latex]15[/latex] from both sides.

[latex]\begin{align*}&\;&30x+15{\color{red}{-}}{\color{red}{15}}&=285{\color{red}{-}}{\color{red}{15}}\\ &\text{Simplify.}\;&30x&=270\\ \end{align*}[/latex]

Step 6: Divide by [latex]30[/latex].

[latex]\begin{align*}&\;&\frac{30x}{\color{red}{30}}&=\frac{270}{\color{red}{30}}\\ &\text{Simplify.}\;&x&=9\\ \end{align*}[/latex]

Step 7: Check it yourself by substituting [latex]x=9[/latex] into the original equation.