Vgln. eerste graad (reeks 3)

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Reeks met haakjes

1. \(4(5x-6)=-6+(-1+x)\)
2. \(3(-2x-5)=12+(-12+x)\)
3. \(3(x-6)=-3-(5+x)\)
4. \(4(-4x+3)=3+(5+x)\)
5. \(6(6x-3)=6-(15+x)\)
6. \(4(-3x-1)=-11+(10+x)\)
7. \(5(-4x+1)=-3-(-8+x)\)
8. \(3(4x-1)=4-(12+x)\)
9. \(3(4x-5)=2+(-9+x)\)
10. \(3(-3x-2)=7-(-13+x)\)
11. \(5(5x-6)=-12-(8+3x)\)
12. \(4(x+1)=10-(9-3x)\)

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (5x-6)& = & -6 \color{red}{+} (-1+x) \\\Leftrightarrow & 20x-24& = &-6-1+x \\\Leftrightarrow & 20x \color{red}{-24} & = &-7 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{-24} \color{blue}{+24} \color{blue}{-x} & = &-7 \color{red}{+x} \color{blue}{-x} \color{blue}{+24} \\\Leftrightarrow & 20x-x& = &-7+24 \\\Leftrightarrow & 19x& = &17 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{17}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{17}{19} & & \\ & V = \left\{ \frac{17}{19} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (-2x-5)& = & 12 \color{red}{+} (-12+x) \\\Leftrightarrow & -6x-15& = &12-12+x \\\Leftrightarrow & -6x \color{red}{-15} & = &0 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{-15} \color{blue}{+15} \color{blue}{-x} & = &0 \color{red}{+x} \color{blue}{-x} \color{blue}{+15} \\\Leftrightarrow & -6x-x& = &0+15 \\\Leftrightarrow & -7x& = &15 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{15}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-15}{7} & & \\ & V = \left\{ \frac{-15}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (x-6)& = & -3 \color{red}{-} (5+x) \\\Leftrightarrow & 3x-18& = &-3-5-x \\\Leftrightarrow & 3x \color{red}{-18} & = &-8 \color{red}{-x} \\\Leftrightarrow & 3x \color{red}{-18} \color{blue}{+18} \color{blue}{+x} & = &-8 \color{red}{-x} \color{blue}{+x} \color{blue}{+18} \\\Leftrightarrow & 3x+x& = &-8+18 \\\Leftrightarrow & 4x& = &10 \\\Leftrightarrow & \frac{4x}{ \color{red}{4} }& = &\frac{10}{ \color{red}{4} } \\\Leftrightarrow & x = \frac{5}{2} & & \\ & V = \left\{ \frac{5}{2} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (-4x+3)& = & 3 \color{red}{+} (5+x) \\\Leftrightarrow & -16x+12& = &3+5+x \\\Leftrightarrow & -16x \color{red}{+12} & = &8 \color{red}{+x} \\\Leftrightarrow & -16x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &8 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & -16x-x& = &8-12 \\\Leftrightarrow & -17x& = &-4 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{-4}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{4}{17} & & \\ & V = \left\{ \frac{4}{17} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (6x-3)& = & 6 \color{red}{-} (15+x) \\\Leftrightarrow & 36x-18& = &6-15-x \\\Leftrightarrow & 36x \color{red}{-18} & = &-9 \color{red}{-x} \\\Leftrightarrow & 36x \color{red}{-18} \color{blue}{+18} \color{blue}{+x} & = &-9 \color{red}{-x} \color{blue}{+x} \color{blue}{+18} \\\Leftrightarrow & 36x+x& = &-9+18 \\\Leftrightarrow & 37x& = &9 \\\Leftrightarrow & \frac{37x}{ \color{red}{37} }& = &\frac{9}{ \color{red}{37} } \\\Leftrightarrow & x = \frac{9}{37} & & \\ & V = \left\{ \frac{9}{37} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (-3x-1)& = & -11 \color{red}{+} (10+x) \\\Leftrightarrow & -12x-4& = &-11+10+x \\\Leftrightarrow & -12x \color{red}{-4} & = &-1 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-4} \color{blue}{+4} \color{blue}{-x} & = &-1 \color{red}{+x} \color{blue}{-x} \color{blue}{+4} \\\Leftrightarrow & -12x-x& = &-1+4 \\\Leftrightarrow & -13x& = &3 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{3}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-3}{13} & & \\ & V = \left\{ \frac{-3}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (-4x+1)& = & -3 \color{red}{-} (-8+x) \\\Leftrightarrow & -20x+5& = &-3+8-x \\\Leftrightarrow & -20x \color{red}{+5} & = &5 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{+5} \color{blue}{-5} \color{blue}{+x} & = &5 \color{red}{-x} \color{blue}{+x} \color{blue}{-5} \\\Leftrightarrow & -20x+x& = &5-5 \\\Leftrightarrow & -19x& = &0 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{0}{ \color{red}{-19} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (4x-1)& = & 4 \color{red}{-} (12+x) \\\Leftrightarrow & 12x-3& = &4-12-x \\\Leftrightarrow & 12x \color{red}{-3} & = &-8 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-3} \color{blue}{+3} \color{blue}{+x} & = &-8 \color{red}{-x} \color{blue}{+x} \color{blue}{+3} \\\Leftrightarrow & 12x+x& = &-8+3 \\\Leftrightarrow & 13x& = &-5 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-5}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-5}{13} & & \\ & V = \left\{ \frac{-5}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (4x-5)& = & 2 \color{red}{+} (-9+x) \\\Leftrightarrow & 12x-15& = &2-9+x \\\Leftrightarrow & 12x \color{red}{-15} & = &-7 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-15} \color{blue}{+15} \color{blue}{-x} & = &-7 \color{red}{+x} \color{blue}{-x} \color{blue}{+15} \\\Leftrightarrow & 12x-x& = &-7+15 \\\Leftrightarrow & 11x& = &8 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{8}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{8}{11} & & \\ & V = \left\{ \frac{8}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (-3x-2)& = & 7 \color{red}{-} (-13+x) \\\Leftrightarrow & -9x-6& = &7+13-x \\\Leftrightarrow & -9x \color{red}{-6} & = &20 \color{red}{-x} \\\Leftrightarrow & -9x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &20 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & -9x+x& = &20+6 \\\Leftrightarrow & -8x& = &26 \\\Leftrightarrow & \frac{-8x}{ \color{red}{-8} }& = &\frac{26}{ \color{red}{-8} } \\\Leftrightarrow & x = \frac{-13}{4} & & \\ & V = \left\{ \frac{-13}{4} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (5x-6)& = & -12 \color{red}{-} (8+3x) \\\Leftrightarrow & 25x-30& = &-12-8-3x \\\Leftrightarrow & 25x \color{red}{-30} & = &-20 \color{red}{-3x} \\\Leftrightarrow & 25x \color{red}{-30} \color{blue}{+30} \color{blue}{+3x} & = &-20 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+30} \\\Leftrightarrow & 25x+3x& = &-20+30 \\\Leftrightarrow & 28x& = &10 \\\Leftrightarrow & \frac{28x}{ \color{red}{28} }& = &\frac{10}{ \color{red}{28} } \\\Leftrightarrow & x = \frac{5}{14} & & \\ & V = \left\{ \frac{5}{14} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (x+1)& = & 10 \color{red}{-} (9-3x) \\\Leftrightarrow & 4x+4& = &10-9+3x \\\Leftrightarrow & 4x \color{red}{+4} & = &1 \color{red}{+3x} \\\Leftrightarrow & 4x \color{red}{+4} \color{blue}{-4} \color{blue}{-3x} & = &1 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-4} \\\Leftrightarrow & 4x-3x& = &1-4 \\\Leftrightarrow & x& = &-3 \\ & V = \left\{ -3 \right\} & \\\end{align}\)