Certainly! Let's solve the given algebraic equations step by step.
### 1. Solving the First Equation
The first equation given is:
[tex]\[ 1.1 - 4x + 10 = -6 \][/tex]
1. Combine the constants on the left-hand side:
[tex]\[ 1.1 + 10 - 4x = -6 \][/tex]
[tex]\[ 11.1 - 4x = -6 \][/tex]
2. Subtract 11.1 from both sides to isolate the term with [tex]\(x\)[/tex]:
[tex]\[ -4x = -6 - 11.1 \][/tex]
[tex]\[ -4x = -17.1 \][/tex]
3. Divide both sides by [tex]\(-4\)[/tex] to solve for [tex]\(x\)[/tex]:
[tex]\[ x = \frac{-17.1}{-4} \][/tex]
[tex]\[ x = 4.275 \][/tex]
So, the solution for the first equation is:
[tex]\[ x = 4.275 \][/tex]
### 2. Solving the Second Equation
The second equation given is:
[tex]\[ \frac{3}{4}a - 5 = -17 \][/tex]
1. Add 5 to both sides to isolate the term with [tex]\(a\)[/tex]:
[tex]\[ \frac{3}{4}a = -17 + 5 \][/tex]
[tex]\[ \frac{3}{4}a = -12 \][/tex]
2. Multiply both sides by the reciprocal of [tex]\(\frac{3}{4}\)[/tex] (which is [tex]\(\frac{4}{3}\)[/tex]) to solve for [tex]\(a\)[/tex]:
[tex]\[ a = -12 \times \frac{4}{3} \][/tex]
[tex]\[ a = -16 \][/tex]
So, the solution for the second equation is:
[tex]\[ a = -16 \][/tex]
### Summary
The solutions to the given equations are:
1. For [tex]\( 1.1 - 4x + 10 = -6 \)[/tex], the value of [tex]\( x \)[/tex] is [tex]\( 4.275 \)[/tex].
2. For [tex]\( \frac{3}{4}a - 5 = -17 \)[/tex], the value of [tex]\( a \)[/tex] is [tex]\( -16 \)[/tex].
