Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (6x+3)& = & -5 \color{red}{+} (1+x) \\\Leftrightarrow & 12x+6& = &-5+1+x \\\Leftrightarrow & 12x \color{red}{+6} & = &-4 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &-4 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & 12x-x& = &-4-6 \\\Leftrightarrow & 11x& = &-10 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-10}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-10}{11} & & \\ & V = \left\{ \frac{-10}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (4x+2)& = & -5 \color{red}{+} (8+3x) \\\Leftrightarrow & 16x+8& = &-5+8+3x \\\Leftrightarrow & 16x \color{red}{+8} & = &3 \color{red}{+3x} \\\Leftrightarrow & 16x \color{red}{+8} \color{blue}{-8} \color{blue}{-3x} & = &3 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-8} \\\Leftrightarrow & 16x-3x& = &3-8 \\\Leftrightarrow & 13x& = &-5 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-5}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-5}{13} & & \\ & V = \left\{ \frac{-5}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (-6x-4)& = & 11 \color{red}{-} (-7+x) \\\Leftrightarrow & -18x-12& = &11+7-x \\\Leftrightarrow & -18x \color{red}{-12} & = &18 \color{red}{-x} \\\Leftrightarrow & -18x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &18 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & -18x+x& = &18+12 \\\Leftrightarrow & -17x& = &30 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{30}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{-30}{17} & & \\ & V = \left\{ \frac{-30}{17} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (-5x+3)& = & -7 \color{red}{+} (11+x) \\\Leftrightarrow & -20x+12& = &-7+11+x \\\Leftrightarrow & -20x \color{red}{+12} & = &4 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &4 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & -20x-x& = &4-12 \\\Leftrightarrow & -21x& = &-8 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{-8}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{8}{21} & & \\ & V = \left\{ \frac{8}{21} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (-6x+5)& = & 12 \color{red}{-} (-14+x) \\\Leftrightarrow & -24x+20& = &12+14-x \\\Leftrightarrow & -24x \color{red}{+20} & = &26 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{+20} \color{blue}{-20} \color{blue}{+x} & = &26 \color{red}{-x} \color{blue}{+x} \color{blue}{-20} \\\Leftrightarrow & -24x+x& = &26-20 \\\Leftrightarrow & -23x& = &6 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{6}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-6}{23} & & \\ & V = \left\{ \frac{-6}{23} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (3x-4)& = & 12 \color{red}{+} (-13-5x) \\\Leftrightarrow & 18x-24& = &12-13-5x \\\Leftrightarrow & 18x \color{red}{-24} & = &-1 \color{red}{-5x} \\\Leftrightarrow & 18x \color{red}{-24} \color{blue}{+24} \color{blue}{+5x} & = &-1 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+24} \\\Leftrightarrow & 18x+5x& = &-1+24 \\\Leftrightarrow & 23x& = &23 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{23}{ \color{red}{23} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (x-6)& = & -14 \color{red}{-} (-14+x) \\\Leftrightarrow & 5x-30& = &-14+14-x \\\Leftrightarrow & 5x \color{red}{-30} & = &0 \color{red}{-x} \\\Leftrightarrow & 5x \color{red}{-30} \color{blue}{+30} \color{blue}{+x} & = &0 \color{red}{-x} \color{blue}{+x} \color{blue}{+30} \\\Leftrightarrow & 5x+x& = &0+30 \\\Leftrightarrow & 6x& = &30 \\\Leftrightarrow & \frac{6x}{ \color{red}{6} }& = &\frac{30}{ \color{red}{6} } \\\Leftrightarrow & x = 5 & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (2x-3)& = & 3 \color{red}{+} (7+x) \\\Leftrightarrow & 8x-12& = &3+7+x \\\Leftrightarrow & 8x \color{red}{-12} & = &10 \color{red}{+x} \\\Leftrightarrow & 8x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &10 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & 8x-x& = &10+12 \\\Leftrightarrow & 7x& = &22 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{22}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{22}{7} & & \\ & V = \left\{ \frac{22}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (-x+6)& = & -7 \color{red}{+} (-7-2x) \\\Leftrightarrow & -5x+30& = &-7-7-2x \\\Leftrightarrow & -5x \color{red}{+30} & = &-14 \color{red}{-2x} \\\Leftrightarrow & -5x \color{red}{+30} \color{blue}{-30} \color{blue}{+2x} & = &-14 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-30} \\\Leftrightarrow & -5x+2x& = &-14-30 \\\Leftrightarrow & -3x& = &-44 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{-44}{ \color{red}{-3} } \\\Leftrightarrow & x = \frac{44}{3} & & \\ & V = \left\{ \frac{44}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (x+4)& = & 4 \color{red}{+} (-2-3x) \\\Leftrightarrow & 4x+16& = &4-2-3x \\\Leftrightarrow & 4x \color{red}{+16} & = &2 \color{red}{-3x} \\\Leftrightarrow & 4x \color{red}{+16} \color{blue}{-16} \color{blue}{+3x} & = &2 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-16} \\\Leftrightarrow & 4x+3x& = &2-16 \\\Leftrightarrow & 7x& = &-14 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-14}{ \color{red}{7} } \\\Leftrightarrow & x = -2 & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (-6x-5)& = & 2 \color{red}{-} (14-5x) \\\Leftrightarrow & -18x-15& = &2-14+5x \\\Leftrightarrow & -18x \color{red}{-15} & = &-12 \color{red}{+5x} \\\Leftrightarrow & -18x \color{red}{-15} \color{blue}{+15} \color{blue}{-5x} & = &-12 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+15} \\\Leftrightarrow & -18x-5x& = &-12+15 \\\Leftrightarrow & -23x& = &3 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{3}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-3}{23} & & \\ & V = \left\{ \frac{-3}{23} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (-5x+6)& = & -6 \color{red}{+} (13+x) \\\Leftrightarrow & -25x+30& = &-6+13+x \\\Leftrightarrow & -25x \color{red}{+30} & = &7 \color{red}{+x} \\\Leftrightarrow & -25x \color{red}{+30} \color{blue}{-30} \color{blue}{-x} & = &7 \color{red}{+x} \color{blue}{-x} \color{blue}{-30} \\\Leftrightarrow & -25x-x& = &7-30 \\\Leftrightarrow & -26x& = &-23 \\\Leftrightarrow & \frac{-26x}{ \color{red}{-26} }& = &\frac{-23}{ \color{red}{-26} } \\\Leftrightarrow & x = \frac{23}{26} & & \\ & V = \left\{ \frac{23}{26} \right\} & \\\end{align}\)