Solve for a. {:[-(1)/(4)a-4=(7)/(4)a-3],[a=◻]:}

Write equation: Write down the given equation. -(1/4)a - 4 = (7/4)a - 3 We need to solve for a by isolating it on one side of the equation.Add terms with a: Add (1/4)a to both sides to start moving all terms with a to one side. -(1/4)a - 4 + (1/4)a = (7/4)a - 3 + (1/4)a This simplifies to: -4 = (7/4)a + (1/4)a - 3Combine like terms: Combine like terms on the right side of the equation. (7/4)a + (1/4)a = (8/4)a This simplifies to: -4 = 2a - 3Isolate term with a: Add 3 to both sides to isolate the term with a. -4 + 3 = 2a - 3 + 3 This simplifies to: -1 = 2aDivide both sides: Divide both sides by 2 to solve for a. -1/2 = a

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Solve for
a.

{:[-(1)/(4)a-4=(7)/(4)a-3],[a=◻]:}

Solve for $a$ . $\newline$ $\begin{array}{l} -\frac{1}{4} a-4=\frac{7}{4} a-3 \\ a=\square \end{array}$

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Math Problems

Algebra 1

Solve linear equations with variables on both sides

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Q. Solve for

a

\newline

\begin{array}{l} -\frac{1}{4} a-4=\frac{7}{4} a-3 \\ a=\square \end{array}

Write equation: Write down the given equation. $\newline$ $-\frac{1}{4}a - 4 = \frac{7}{4}a - 3$ $\newline$ We need to solve for $a$ by isolating it on one side of the equation.
Add terms with a: Add $(\frac{1}{4})a$ to both sides to start moving all terms with a to one side. $\newline$ -\left(\frac{1}{4}\right)a - 4 + \left(\frac{1}{4}\right)a = \left(\frac{7}{4}\right)a - 3 + \left(\frac{1}{4}\right)a$\newlineThis simplifies to: $\newline$ \$-4 = \left(\frac{7}{4}\right)a + \left(\frac{1}{4}\right)a - 3$
Combine like terms: Combine like terms on the right side of the equation.$\newline$$(\frac{7}{4})a + (\frac{1}{4})a = (\frac{8}{4})a$$\newline$This simplifies to:$\newline$$-4 = 2a - 3$
Isolate term with $a$: Add $3$ to both sides to isolate the term with $a$.
$-4 + 3 = 2a - 3 + 3$
This simplifies to:
$-1 = 2a$
Divide both sides: Divide both sides by $2$ to solve for $a$.$\newline$$-\frac{1}{2} = a$