Vgln. eerste graad (reeks 3)

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Reeks met haakjes

1. \(2(-2x+6)=15-(-6+3x)\)
2. \(5(-4x-2)=3+(9+3x)\)
3. \(6(5x-7)=-14+(-9+x)\)
4. \(3(6x-4)=-9-(-10+x)\)
5. \(5(5x-2)=13+(8+2x)\)
6. \(6(5x+3)=-4-(-10+x)\)
7. \(2(5x+6)=7-(4+3x)\)
8. \(6(x-2)=4-(4+x)\)
9. \(5(-3x-3)=-8-(-2+4x)\)
10. \(2(-4x-3)=5-(12+3x)\)
11. \(2(-5x-7)=6+(-8+3x)\)
12. \(6(2x+5)=-13+(-1+x)\)

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (-2x+6)& = & 15 \color{red}{-} (-6+3x) \\\Leftrightarrow & -4x+12& = &15+6-3x \\\Leftrightarrow & -4x \color{red}{+12} & = &21 \color{red}{-3x} \\\Leftrightarrow & -4x \color{red}{+12} \color{blue}{-12} \color{blue}{+3x} & = &21 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-12} \\\Leftrightarrow & -4x+3x& = &21-12 \\\Leftrightarrow & -x& = &9 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{9}{ \color{red}{-1} } \\\Leftrightarrow & x = -9 & & \\ & V = \left\{ -9 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (-4x-2)& = & 3 \color{red}{+} (9+3x) \\\Leftrightarrow & -20x-10& = &3+9+3x \\\Leftrightarrow & -20x \color{red}{-10} & = &12 \color{red}{+3x} \\\Leftrightarrow & -20x \color{red}{-10} \color{blue}{+10} \color{blue}{-3x} & = &12 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+10} \\\Leftrightarrow & -20x-3x& = &12+10 \\\Leftrightarrow & -23x& = &22 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{22}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-22}{23} & & \\ & V = \left\{ \frac{-22}{23} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (5x-7)& = & -14 \color{red}{+} (-9+x) \\\Leftrightarrow & 30x-42& = &-14-9+x \\\Leftrightarrow & 30x \color{red}{-42} & = &-23 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{-42} \color{blue}{+42} \color{blue}{-x} & = &-23 \color{red}{+x} \color{blue}{-x} \color{blue}{+42} \\\Leftrightarrow & 30x-x& = &-23+42 \\\Leftrightarrow & 29x& = &19 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{19}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{19}{29} & & \\ & V = \left\{ \frac{19}{29} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (6x-4)& = & -9 \color{red}{-} (-10+x) \\\Leftrightarrow & 18x-12& = &-9+10-x \\\Leftrightarrow & 18x \color{red}{-12} & = &1 \color{red}{-x} \\\Leftrightarrow & 18x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &1 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & 18x+x& = &1+12 \\\Leftrightarrow & 19x& = &13 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{13}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{13}{19} & & \\ & V = \left\{ \frac{13}{19} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (5x-2)& = & 13 \color{red}{+} (8+2x) \\\Leftrightarrow & 25x-10& = &13+8+2x \\\Leftrightarrow & 25x \color{red}{-10} & = &21 \color{red}{+2x} \\\Leftrightarrow & 25x \color{red}{-10} \color{blue}{+10} \color{blue}{-2x} & = &21 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+10} \\\Leftrightarrow & 25x-2x& = &21+10 \\\Leftrightarrow & 23x& = &31 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{31}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{31}{23} & & \\ & V = \left\{ \frac{31}{23} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (5x+3)& = & -4 \color{red}{-} (-10+x) \\\Leftrightarrow & 30x+18& = &-4+10-x \\\Leftrightarrow & 30x \color{red}{+18} & = &6 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{+18} \color{blue}{-18} \color{blue}{+x} & = &6 \color{red}{-x} \color{blue}{+x} \color{blue}{-18} \\\Leftrightarrow & 30x+x& = &6-18 \\\Leftrightarrow & 31x& = &-12 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{-12}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{-12}{31} & & \\ & V = \left\{ \frac{-12}{31} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (5x+6)& = & 7 \color{red}{-} (4+3x) \\\Leftrightarrow & 10x+12& = &7-4-3x \\\Leftrightarrow & 10x \color{red}{+12} & = &3 \color{red}{-3x} \\\Leftrightarrow & 10x \color{red}{+12} \color{blue}{-12} \color{blue}{+3x} & = &3 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-12} \\\Leftrightarrow & 10x+3x& = &3-12 \\\Leftrightarrow & 13x& = &-9 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-9}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-9}{13} & & \\ & V = \left\{ \frac{-9}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (x-2)& = & 4 \color{red}{-} (4+x) \\\Leftrightarrow & 6x-12& = &4-4-x \\\Leftrightarrow & 6x \color{red}{-12} & = &0 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &0 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & 6x+x& = &0+12 \\\Leftrightarrow & 7x& = &12 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{12}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{12}{7} & & \\ & V = \left\{ \frac{12}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (-3x-3)& = & -8 \color{red}{-} (-2+4x) \\\Leftrightarrow & -15x-15& = &-8+2-4x \\\Leftrightarrow & -15x \color{red}{-15} & = &-6 \color{red}{-4x} \\\Leftrightarrow & -15x \color{red}{-15} \color{blue}{+15} \color{blue}{+4x} & = &-6 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+15} \\\Leftrightarrow & -15x+4x& = &-6+15 \\\Leftrightarrow & -11x& = &9 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{9}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-9}{11} & & \\ & V = \left\{ \frac{-9}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (-4x-3)& = & 5 \color{red}{-} (12+3x) \\\Leftrightarrow & -8x-6& = &5-12-3x \\\Leftrightarrow & -8x \color{red}{-6} & = &-7 \color{red}{-3x} \\\Leftrightarrow & -8x \color{red}{-6} \color{blue}{+6} \color{blue}{+3x} & = &-7 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+6} \\\Leftrightarrow & -8x+3x& = &-7+6 \\\Leftrightarrow & -5x& = &-1 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-1}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{1}{5} & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (-5x-7)& = & 6 \color{red}{+} (-8+3x) \\\Leftrightarrow & -10x-14& = &6-8+3x \\\Leftrightarrow & -10x \color{red}{-14} & = &-2 \color{red}{+3x} \\\Leftrightarrow & -10x \color{red}{-14} \color{blue}{+14} \color{blue}{-3x} & = &-2 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+14} \\\Leftrightarrow & -10x-3x& = &-2+14 \\\Leftrightarrow & -13x& = &12 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{12}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-12}{13} & & \\ & V = \left\{ \frac{-12}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (2x+5)& = & -13 \color{red}{+} (-1+x) \\\Leftrightarrow & 12x+30& = &-13-1+x \\\Leftrightarrow & 12x \color{red}{+30} & = &-14 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+30} \color{blue}{-30} \color{blue}{-x} & = &-14 \color{red}{+x} \color{blue}{-x} \color{blue}{-30} \\\Leftrightarrow & 12x-x& = &-14-30 \\\Leftrightarrow & 11x& = &-44 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-44}{ \color{red}{11} } \\\Leftrightarrow & x = -4 & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)