Absolutely, let's solve these equations step-by-step:
### (a)
Solve the equation [tex]\( 5x - (3x - 1) = 23 \)[/tex]:
1. Distribute the terms inside the parentheses:
[tex]\( 5x - 3x + 1 = 23 \)[/tex]
2. Combine like terms:
[tex]\( (5x - 3x) + 1 = 23 \)[/tex]
[tex]\( 2x + 1 = 23 \)[/tex]
3. Subtract 1 from both sides:
[tex]\( 2x = 22 \)[/tex]
4. Divide both sides by 2:
[tex]\( x = 11 \)[/tex]
So, the solution to this equation is [tex]\( x = 11 \)[/tex].
### (б)
Solve the equation [tex]\( 4 - (5 - x) - (3x - 6) = 0 \)[/tex]:
1. Distribute the terms inside the parentheses:
[tex]\( 4 - 5 + x - 3x + 6 = 0 \)[/tex]
2. Combine like terms:
[tex]\( (4 - 5 + 6) + (x - 3x) = 0 \)[/tex]
[tex]\( 5 - 2x = 0 \)[/tex]
3. Subtract 5 from both sides:
[tex]\( -2x = -5 \)[/tex]
4. Divide both sides by -2:
[tex]\( x = \frac{5}{2} \)[/tex]
So, the solution to this equation is [tex]\( x = \frac{5}{2} \)[/tex].
### (в)
Solve the equation [tex]\( 3(y - 5) - 4(y - 4) = 8 \)[/tex]:
1. Distribute the terms inside the parentheses:
[tex]\( 3y - 15 - 4y + 16 = 8 \)[/tex]
2. Combine like terms:
[tex]\( (3y - 4y) + (-15 + 16) = 8 \)[/tex]
[tex]\( -y + 1 = 8 \)[/tex]
3. Subtract 1 from both sides:
[tex]\( -y = 7 \)[/tex]
4. Multiply both sides by -1:
[tex]\( y = -7 \)[/tex]
So, the solution to this equation is [tex]\( y = -7 \)[/tex].
### (2)
Solve the equation [tex]\( 8(y - 5) + 2(5y - 4) = 10 \)[/tex]:
1. Distribute the terms inside the parentheses:
[tex]\( 8y - 40 + 10y - 8 = 10 \)[/tex]
2. Combine like terms:
[tex]\( (8y + 10y) + (-40 - 8) = 10 \)[/tex]
[tex]\( 18y - 48 = 10 \)[/tex]
3. Add 48 to both sides:
[tex]\( 18y = 58 \)[/tex]
4. Divide both sides by 18:
[tex]\( y = \frac{58}{18} \)[/tex]
5. Simplify the fraction:
[tex]\( y = \frac{29}{9} \)[/tex]
So, the solution to this equation is [tex]\( y = \frac{29}{9} \)[/tex].
In summary, the solutions to the equations are:
a) [tex]\( x = 11 \)[/tex]
б) [tex]\( x = \frac{5}{2} \)[/tex]
в) [tex]\( y = -7 \)[/tex]
2) [tex]\( y = \frac{29}{9} \)[/tex]
