Vgln. eerste graad (reeks 3)

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Reeks met haakjes

1. \(3(-x+1)=-3-(12+2x)\)
2. \(2(-3x+1)=-8-(-4+x)\)
3. \(2(x+3)=1-(-10+x)\)
4. \(4(6x+7)=11-(-9+x)\)
5. \(6(-3x+4)=-3-(5+x)\)
6. \(5(x+3)=-6-(-5+4x)\)
7. \(3(-5x-6)=-1+(2-2x)\)
8. \(5(-2x-3)=-6+(6+x)\)
9. \(3(5x+1)=3-(4+4x)\)
10. \(6(3x-7)=-7+(-15+x)\)
11. \(6(4x+5)=-3-(3+x)\)
12. \(3(4x+7)=-4+(12+x)\)

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (-x+1)& = & -3 \color{red}{-} (12+2x) \\\Leftrightarrow & -3x+3& = &-3-12-2x \\\Leftrightarrow & -3x \color{red}{+3} & = &-15 \color{red}{-2x} \\\Leftrightarrow & -3x \color{red}{+3} \color{blue}{-3} \color{blue}{+2x} & = &-15 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-3} \\\Leftrightarrow & -3x+2x& = &-15-3 \\\Leftrightarrow & -x& = &-18 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-18}{ \color{red}{-1} } \\\Leftrightarrow & x = 18 & & \\ & V = \left\{ 18 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (-3x+1)& = & -8 \color{red}{-} (-4+x) \\\Leftrightarrow & -6x+2& = &-8+4-x \\\Leftrightarrow & -6x \color{red}{+2} & = &-4 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{+2} \color{blue}{-2} \color{blue}{+x} & = &-4 \color{red}{-x} \color{blue}{+x} \color{blue}{-2} \\\Leftrightarrow & -6x+x& = &-4-2 \\\Leftrightarrow & -5x& = &-6 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-6}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{6}{5} & & \\ & V = \left\{ \frac{6}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (x+3)& = & 1 \color{red}{-} (-10+x) \\\Leftrightarrow & 2x+6& = &1+10-x \\\Leftrightarrow & 2x \color{red}{+6} & = &11 \color{red}{-x} \\\Leftrightarrow & 2x \color{red}{+6} \color{blue}{-6} \color{blue}{+x} & = &11 \color{red}{-x} \color{blue}{+x} \color{blue}{-6} \\\Leftrightarrow & 2x+x& = &11-6 \\\Leftrightarrow & 3x& = &5 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{5}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{5}{3} & & \\ & V = \left\{ \frac{5}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (6x+7)& = & 11 \color{red}{-} (-9+x) \\\Leftrightarrow & 24x+28& = &11+9-x \\\Leftrightarrow & 24x \color{red}{+28} & = &20 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{+28} \color{blue}{-28} \color{blue}{+x} & = &20 \color{red}{-x} \color{blue}{+x} \color{blue}{-28} \\\Leftrightarrow & 24x+x& = &20-28 \\\Leftrightarrow & 25x& = &-8 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{-8}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{-8}{25} & & \\ & V = \left\{ \frac{-8}{25} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (-3x+4)& = & -3 \color{red}{-} (5+x) \\\Leftrightarrow & -18x+24& = &-3-5-x \\\Leftrightarrow & -18x \color{red}{+24} & = &-8 \color{red}{-x} \\\Leftrightarrow & -18x \color{red}{+24} \color{blue}{-24} \color{blue}{+x} & = &-8 \color{red}{-x} \color{blue}{+x} \color{blue}{-24} \\\Leftrightarrow & -18x+x& = &-8-24 \\\Leftrightarrow & -17x& = &-32 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{-32}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{32}{17} & & \\ & V = \left\{ \frac{32}{17} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (x+3)& = & -6 \color{red}{-} (-5+4x) \\\Leftrightarrow & 5x+15& = &-6+5-4x \\\Leftrightarrow & 5x \color{red}{+15} & = &-1 \color{red}{-4x} \\\Leftrightarrow & 5x \color{red}{+15} \color{blue}{-15} \color{blue}{+4x} & = &-1 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-15} \\\Leftrightarrow & 5x+4x& = &-1-15 \\\Leftrightarrow & 9x& = &-16 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{-16}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{-16}{9} & & \\ & V = \left\{ \frac{-16}{9} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (-5x-6)& = & -1 \color{red}{+} (2-2x) \\\Leftrightarrow & -15x-18& = &-1+2-2x \\\Leftrightarrow & -15x \color{red}{-18} & = &1 \color{red}{-2x} \\\Leftrightarrow & -15x \color{red}{-18} \color{blue}{+18} \color{blue}{+2x} & = &1 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+18} \\\Leftrightarrow & -15x+2x& = &1+18 \\\Leftrightarrow & -13x& = &19 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{19}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-19}{13} & & \\ & V = \left\{ \frac{-19}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (-2x-3)& = & -6 \color{red}{+} (6+x) \\\Leftrightarrow & -10x-15& = &-6+6+x \\\Leftrightarrow & -10x \color{red}{-15} & = &0 \color{red}{+x} \\\Leftrightarrow & -10x \color{red}{-15} \color{blue}{+15} \color{blue}{-x} & = &0 \color{red}{+x} \color{blue}{-x} \color{blue}{+15} \\\Leftrightarrow & -10x-x& = &0+15 \\\Leftrightarrow & -11x& = &15 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{15}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-15}{11} & & \\ & V = \left\{ \frac{-15}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (5x+1)& = & 3 \color{red}{-} (4+4x) \\\Leftrightarrow & 15x+3& = &3-4-4x \\\Leftrightarrow & 15x \color{red}{+3} & = &-1 \color{red}{-4x} \\\Leftrightarrow & 15x \color{red}{+3} \color{blue}{-3} \color{blue}{+4x} & = &-1 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-3} \\\Leftrightarrow & 15x+4x& = &-1-3 \\\Leftrightarrow & 19x& = &-4 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-4}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-4}{19} & & \\ & V = \left\{ \frac{-4}{19} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (3x-7)& = & -7 \color{red}{+} (-15+x) \\\Leftrightarrow & 18x-42& = &-7-15+x \\\Leftrightarrow & 18x \color{red}{-42} & = &-22 \color{red}{+x} \\\Leftrightarrow & 18x \color{red}{-42} \color{blue}{+42} \color{blue}{-x} & = &-22 \color{red}{+x} \color{blue}{-x} \color{blue}{+42} \\\Leftrightarrow & 18x-x& = &-22+42 \\\Leftrightarrow & 17x& = &20 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{20}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{20}{17} & & \\ & V = \left\{ \frac{20}{17} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (4x+5)& = & -3 \color{red}{-} (3+x) \\\Leftrightarrow & 24x+30& = &-3-3-x \\\Leftrightarrow & 24x \color{red}{+30} & = &-6 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{+30} \color{blue}{-30} \color{blue}{+x} & = &-6 \color{red}{-x} \color{blue}{+x} \color{blue}{-30} \\\Leftrightarrow & 24x+x& = &-6-30 \\\Leftrightarrow & 25x& = &-36 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{-36}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{-36}{25} & & \\ & V = \left\{ \frac{-36}{25} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (4x+7)& = & -4 \color{red}{+} (12+x) \\\Leftrightarrow & 12x+21& = &-4+12+x \\\Leftrightarrow & 12x \color{red}{+21} & = &8 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+21} \color{blue}{-21} \color{blue}{-x} & = &8 \color{red}{+x} \color{blue}{-x} \color{blue}{-21} \\\Leftrightarrow & 12x-x& = &8-21 \\\Leftrightarrow & 11x& = &-13 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-13}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-13}{11} & & \\ & V = \left\{ \frac{-13}{11} \right\} & \\\end{align}\)