Vgln. eerste graad (reeks 3)

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Reeks met haakjes

1. \(6(5x-1)=8-(10+x)\)
2. \(6(5x+2)=-14+(6+x)\)
3. \(5(-5x-4)=9+(6+3x)\)
4. \(6(6x+7)=3-(-11-5x)\)
5. \(5(3x+3)=-15-(-8+x)\)
6. \(5(6x+2)=-7-(14+x)\)
7. \(2(3x+7)=-7+(6+x)\)
8. \(4(x-5)=-8+(-9-3x)\)
9. \(2(2x+5)=11-(-10-3x)\)
10. \(5(5x+7)=3+(-6-2x)\)
11. \(3(4x-6)=-10+(-7+x)\)
12. \(4(4x-1)=-12+(10-3x)\)

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (5x-1)& = & 8 \color{red}{-} (10+x) \\\Leftrightarrow & 30x-6& = &8-10-x \\\Leftrightarrow & 30x \color{red}{-6} & = &-2 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &-2 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & 30x+x& = &-2+6 \\\Leftrightarrow & 31x& = &4 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{4}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{4}{31} & & \\ & V = \left\{ \frac{4}{31} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (5x+2)& = & -14 \color{red}{+} (6+x) \\\Leftrightarrow & 30x+12& = &-14+6+x \\\Leftrightarrow & 30x \color{red}{+12} & = &-8 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &-8 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & 30x-x& = &-8-12 \\\Leftrightarrow & 29x& = &-20 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{-20}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{-20}{29} & & \\ & V = \left\{ \frac{-20}{29} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (-5x-4)& = & 9 \color{red}{+} (6+3x) \\\Leftrightarrow & -25x-20& = &9+6+3x \\\Leftrightarrow & -25x \color{red}{-20} & = &15 \color{red}{+3x} \\\Leftrightarrow & -25x \color{red}{-20} \color{blue}{+20} \color{blue}{-3x} & = &15 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+20} \\\Leftrightarrow & -25x-3x& = &15+20 \\\Leftrightarrow & -28x& = &35 \\\Leftrightarrow & \frac{-28x}{ \color{red}{-28} }& = &\frac{35}{ \color{red}{-28} } \\\Leftrightarrow & x = \frac{-5}{4} & & \\ & V = \left\{ \frac{-5}{4} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (6x+7)& = & 3 \color{red}{-} (-11-5x) \\\Leftrightarrow & 36x+42& = &3+11+5x \\\Leftrightarrow & 36x \color{red}{+42} & = &14 \color{red}{+5x} \\\Leftrightarrow & 36x \color{red}{+42} \color{blue}{-42} \color{blue}{-5x} & = &14 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-42} \\\Leftrightarrow & 36x-5x& = &14-42 \\\Leftrightarrow & 31x& = &-28 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{-28}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{-28}{31} & & \\ & V = \left\{ \frac{-28}{31} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (3x+3)& = & -15 \color{red}{-} (-8+x) \\\Leftrightarrow & 15x+15& = &-15+8-x \\\Leftrightarrow & 15x \color{red}{+15} & = &-7 \color{red}{-x} \\\Leftrightarrow & 15x \color{red}{+15} \color{blue}{-15} \color{blue}{+x} & = &-7 \color{red}{-x} \color{blue}{+x} \color{blue}{-15} \\\Leftrightarrow & 15x+x& = &-7-15 \\\Leftrightarrow & 16x& = &-22 \\\Leftrightarrow & \frac{16x}{ \color{red}{16} }& = &\frac{-22}{ \color{red}{16} } \\\Leftrightarrow & x = \frac{-11}{8} & & \\ & V = \left\{ \frac{-11}{8} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (6x+2)& = & -7 \color{red}{-} (14+x) \\\Leftrightarrow & 30x+10& = &-7-14-x \\\Leftrightarrow & 30x \color{red}{+10} & = &-21 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{+10} \color{blue}{-10} \color{blue}{+x} & = &-21 \color{red}{-x} \color{blue}{+x} \color{blue}{-10} \\\Leftrightarrow & 30x+x& = &-21-10 \\\Leftrightarrow & 31x& = &-31 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{-31}{ \color{red}{31} } \\\Leftrightarrow & x = -1 & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (3x+7)& = & -7 \color{red}{+} (6+x) \\\Leftrightarrow & 6x+14& = &-7+6+x \\\Leftrightarrow & 6x \color{red}{+14} & = &-1 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{+14} \color{blue}{-14} \color{blue}{-x} & = &-1 \color{red}{+x} \color{blue}{-x} \color{blue}{-14} \\\Leftrightarrow & 6x-x& = &-1-14 \\\Leftrightarrow & 5x& = &-15 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-15}{ \color{red}{5} } \\\Leftrightarrow & x = -3 & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (x-5)& = & -8 \color{red}{+} (-9-3x) \\\Leftrightarrow & 4x-20& = &-8-9-3x \\\Leftrightarrow & 4x \color{red}{-20} & = &-17 \color{red}{-3x} \\\Leftrightarrow & 4x \color{red}{-20} \color{blue}{+20} \color{blue}{+3x} & = &-17 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+20} \\\Leftrightarrow & 4x+3x& = &-17+20 \\\Leftrightarrow & 7x& = &3 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{3}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{3}{7} & & \\ & V = \left\{ \frac{3}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (2x+5)& = & 11 \color{red}{-} (-10-3x) \\\Leftrightarrow & 4x+10& = &11+10+3x \\\Leftrightarrow & 4x \color{red}{+10} & = &21 \color{red}{+3x} \\\Leftrightarrow & 4x \color{red}{+10} \color{blue}{-10} \color{blue}{-3x} & = &21 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-10} \\\Leftrightarrow & 4x-3x& = &21-10 \\\Leftrightarrow & x& = &11 \\ & V = \left\{ 11 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (5x+7)& = & 3 \color{red}{+} (-6-2x) \\\Leftrightarrow & 25x+35& = &3-6-2x \\\Leftrightarrow & 25x \color{red}{+35} & = &-3 \color{red}{-2x} \\\Leftrightarrow & 25x \color{red}{+35} \color{blue}{-35} \color{blue}{+2x} & = &-3 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-35} \\\Leftrightarrow & 25x+2x& = &-3-35 \\\Leftrightarrow & 27x& = &-38 \\\Leftrightarrow & \frac{27x}{ \color{red}{27} }& = &\frac{-38}{ \color{red}{27} } \\\Leftrightarrow & x = \frac{-38}{27} & & \\ & V = \left\{ \frac{-38}{27} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (4x-6)& = & -10 \color{red}{+} (-7+x) \\\Leftrightarrow & 12x-18& = &-10-7+x \\\Leftrightarrow & 12x \color{red}{-18} & = &-17 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-18} \color{blue}{+18} \color{blue}{-x} & = &-17 \color{red}{+x} \color{blue}{-x} \color{blue}{+18} \\\Leftrightarrow & 12x-x& = &-17+18 \\\Leftrightarrow & 11x& = &1 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{1}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{1}{11} & & \\ & V = \left\{ \frac{1}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (4x-1)& = & -12 \color{red}{+} (10-3x) \\\Leftrightarrow & 16x-4& = &-12+10-3x \\\Leftrightarrow & 16x \color{red}{-4} & = &-2 \color{red}{-3x} \\\Leftrightarrow & 16x \color{red}{-4} \color{blue}{+4} \color{blue}{+3x} & = &-2 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+4} \\\Leftrightarrow & 16x+3x& = &-2+4 \\\Leftrightarrow & 19x& = &2 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{2}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{2}{19} & & \\ & V = \left\{ \frac{2}{19} \right\} & \\\end{align}\)