Sure! Let's solve the given equation step-by-step:
The given equation is:
[tex]\[ 24a - 22 = -4(1 - 6a) \][/tex]
Step 1: Distribute the -4 on the right-hand side:
[tex]\[ 24a - 22 = -4 \cdot 1 + (-4) \cdot (-6a) \][/tex]
[tex]\[ 24a - 22 = -4 + 24a \][/tex]
Step 2: Simplify both sides.
[tex]\[ 24a - 22 = -4 + 24a \][/tex]
Step 3: Notice that both sides of the equation have the same variable term [tex]\( 24a \)[/tex]. Subtract [tex]\( 24a \)[/tex] from both sides to eliminate it:
[tex]\[ 24a - 22 - 24a = -4 + 24a - 24a \][/tex]
[tex]\[ -22 = -4 \][/tex]
Step 4: Notice that we are left with a false statement, [tex]\(-22\)[/tex] does not equal [tex]\(-4\)[/tex].
When you reach a false statement like this, it indicates that the original equation has no solution. Therefore, there is no value of [tex]\( a \)[/tex] that will satisfy the given equation.
In conclusion, the equation [tex]\( 24a - 22 = -4(1 - 6a) \)[/tex] has no solution.
