Question

kuta software - infinite algebra 1
literal equations
solve each equation for the indicated variable.

1. $g = 6x$, for $x$
2. $u = 2x - 2$, for $x$
3. $z = m - x$, for $x$
4. $g = ca$, for $a$
5. $u = x - k$, for $x$
6. $g = c + x$, for $x$
7. $u = \frac{k}{a}$, for $a$
8. $g = xc$, for $x$
9. $12am = 4$, for $a$
10. $-3x + 2c = -3$, for $x$
11. $am = n + p$, for $a$
12. $u = \frac{ak}{b}$, for $a$
13. $a - c = d - r$, for $a$
14. $xm = np$, for $x$

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Explanation:

Let's solve each equation one by one:

1) \( g = 6x \), for \( x \)

Step 1: Isolate \( x \)

Divide both sides by 6:
\( \frac{g}{6} = x \) or \( x = \frac{g}{6} \)

2) \( u = 2x - 2 \), for \( x \)

Step 1: Add 2 to both sides

\( u + 2 = 2x \)

Step 2: Divide by 2

\( x = \frac{u + 2}{2} = \frac{u}{2} + 1 \)

3) \( z = m - x \) (assuming the first variable is \( z \)), for \( x \)

Step 1: Rearrange to isolate \( x \)

Add \( x \) to both sides: \( z + x = m \)
Subtract \( z \) from both sides: \( x = m - z \)

4) \( g = ca \), for \( a \)

Step 1: Divide by \( c \) ( \( c

eq 0 \) )
\( a = \frac{g}{c} \)

5) \( u = x - k \), for \( x \)

Step 1: Add \( k \) to both sides

\( x = u + k \)

6) \( g = c + x \), for \( x \)

Step 1: Subtract \( c \) from both sides

\( x = g - c \)

7) \( u = \frac{k}{a} \), for \( a \)

Step 1: Multiply both sides by \( a \)

\( ua = k \)

Step 2: Divide by \( u \) ( \( u

eq 0 \) )
\( a = \frac{k}{u} \)

8) \( g = xc \), for \( x \)

Step 1: Divide by \( c \) ( \( c

eq 0 \) )
\( x = \frac{g}{c} \)

9) \( 12am = 4 \), for \( a \)

Step 1: Divide by \( 12m \) ( \( m

eq 0 \) )
\( a = \frac{4}{12m} = \frac{1}{3m} \)

10) \( -3x + 2c = -3 \), for \( x \)

Step 1: Subtract \( 2c \) from both sides

\( -3x = -3 - 2c \)

Step 2: Divide by \( -3 \)

\( x = \frac{-3 - 2c}{-3} = 1 + \frac{2c}{3} \)

11) \( am = n + p \), for \( a \)

Step 1: Divide by \( m \) ( \( m

eq 0 \) )
\( a = \frac{n + p}{m} \)

12) \( u = \frac{ak}{b} \), for \( a \)

Step 1: Multiply both sides by \( b \)

\( ub = ak \)

Step 2: Divide by \( k \) ( \( k

eq 0 \) )
\( a = \frac{ub}{k} \)

13) \( a - c = d - r \), for \( a \)

Step 1: Add \( c \) to both sides

\( a = d - r + c \)

14) \( xm = np \), for \( x \)

Step 1: Divide by \( m \) ( \( m

eq 0 \) )
\( x = \frac{np}{m} \)

Final Answers:

1. \( \boldsymbol{x = \frac{g}{6}} \)
2. \( \boldsymbol{x = \frac{u + 2}{2}} \) (or \( \boldsymbol{x = \frac{u}{2} + 1} \))
3. \( \boldsymbol{x = m - z} \)
4. \( \boldsymbol{a = \frac{g}{c}} \)
5. \( \boldsymbol{x = u + k} \)
6. \( \boldsymbol{x = g - c} \)
7. \( \boldsymbol{a = \frac{k}{u}} \)
8. \( \boldsymbol{x = \frac{g}{c}} \)
9. \( \boldsymbol{a = \frac{1}{3m}} \)
10. \( \boldsymbol{x = 1 + \frac{2c}{3}} \) (or \( \boldsymbol{x = \frac{2c + 3}{3}} \))
11. \( \boldsymbol{a = \frac{n + p}{m}} \)
12. \( \boldsymbol{a = \frac{ub}{k}} \)
13. \( \boldsymbol{a = c + d - r} \)
14. \( \boldsymbol{x = \frac{np}{m}} \)

Answer:

Let's solve each equation one by one:

1) \( g = 6x \), for \( x \)

Step 1: Isolate \( x \)

Divide both sides by 6:
\( \frac{g}{6} = x \) or \( x = \frac{g}{6} \)

2) \( u = 2x - 2 \), for \( x \)

Step 1: Add 2 to both sides

\( u + 2 = 2x \)

Step 2: Divide by 2

\( x = \frac{u + 2}{2} = \frac{u}{2} + 1 \)

3) \( z = m - x \) (assuming the first variable is \( z \)), for \( x \)

Step 1: Rearrange to isolate \( x \)

Add \( x \) to both sides: \( z + x = m \)
Subtract \( z \) from both sides: \( x = m - z \)

4) \( g = ca \), for \( a \)

Step 1: Divide by \( c \) ( \( c

eq 0 \) )
\( a = \frac{g}{c} \)

5) \( u = x - k \), for \( x \)

Step 1: Add \( k \) to both sides

\( x = u + k \)

6) \( g = c + x \), for \( x \)

Step 1: Subtract \( c \) from both sides

\( x = g - c \)

7) \( u = \frac{k}{a} \), for \( a \)

Step 1: Multiply both sides by \( a \)

\( ua = k \)

Step 2: Divide by \( u \) ( \( u

eq 0 \) )
\( a = \frac{k}{u} \)

8) \( g = xc \), for \( x \)

Step 1: Divide by \( c \) ( \( c

eq 0 \) )
\( x = \frac{g}{c} \)

9) \( 12am = 4 \), for \( a \)

Step 1: Divide by \( 12m \) ( \( m

eq 0 \) )
\( a = \frac{4}{12m} = \frac{1}{3m} \)

10) \( -3x + 2c = -3 \), for \( x \)

Step 1: Subtract \( 2c \) from both sides

\( -3x = -3 - 2c \)

Step 2: Divide by \( -3 \)

\( x = \frac{-3 - 2c}{-3} = 1 + \frac{2c}{3} \)

11) \( am = n + p \), for \( a \)

Step 1: Divide by \( m \) ( \( m

eq 0 \) )
\( a = \frac{n + p}{m} \)

12) \( u = \frac{ak}{b} \), for \( a \)

Step 1: Multiply both sides by \( b \)

\( ub = ak \)

Step 2: Divide by \( k \) ( \( k

eq 0 \) )
\( a = \frac{ub}{k} \)

13) \( a - c = d - r \), for \( a \)

Step 1: Add \( c \) to both sides

\( a = d - r + c \)

14) \( xm = np \), for \( x \)

Step 1: Divide by \( m \) ( \( m

eq 0 \) )
\( x = \frac{np}{m} \)

Final Answers:

1. \( \boldsymbol{x = \frac{g}{6}} \)
2. \( \boldsymbol{x = \frac{u + 2}{2}} \) (or \( \boldsymbol{x = \frac{u}{2} + 1} \))
3. \( \boldsymbol{x = m - z} \)
4. \( \boldsymbol{a = \frac{g}{c}} \)
5. \( \boldsymbol{x = u + k} \)
6. \( \boldsymbol{x = g - c} \)
7. \( \boldsymbol{a = \frac{k}{u}} \)
8. \( \boldsymbol{x = \frac{g}{c}} \)
9. \( \boldsymbol{a = \frac{1}{3m}} \)
10. \( \boldsymbol{x = 1 + \frac{2c}{3}} \) (or \( \boldsymbol{x = \frac{2c + 3}{3}} \))
11. \( \boldsymbol{a = \frac{n + p}{m}} \)
12. \( \boldsymbol{a = \frac{ub}{k}} \)
13. \( \boldsymbol{a = c + d - r} \)
14. \( \boldsymbol{x = \frac{np}{m}} \)