Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (x-5)& = & -2 \color{red}{-} (-12+x) \\\Leftrightarrow & 4x-20& = &-2+12-x \\\Leftrightarrow & 4x \color{red}{-20} & = &10 \color{red}{-x} \\\Leftrightarrow & 4x \color{red}{-20} \color{blue}{+20} \color{blue}{+x} & = &10 \color{red}{-x} \color{blue}{+x} \color{blue}{+20} \\\Leftrightarrow & 4x+x& = &10+20 \\\Leftrightarrow & 5x& = &30 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{30}{ \color{red}{5} } \\\Leftrightarrow & x = 6 & & \\ & V = \left\{ 6 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (-3x-2)& = & -4 \color{red}{-} (-1+x) \\\Leftrightarrow & -18x-12& = &-4+1-x \\\Leftrightarrow & -18x \color{red}{-12} & = &-3 \color{red}{-x} \\\Leftrightarrow & -18x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &-3 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & -18x+x& = &-3+12 \\\Leftrightarrow & -17x& = &9 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{9}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{-9}{17} & & \\ & V = \left\{ \frac{-9}{17} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (-4x+3)& = & 9 \color{red}{-} (-1+x) \\\Leftrightarrow & -12x+9& = &9+1-x \\\Leftrightarrow & -12x \color{red}{+9} & = &10 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+9} \color{blue}{-9} \color{blue}{+x} & = &10 \color{red}{-x} \color{blue}{+x} \color{blue}{-9} \\\Leftrightarrow & -12x+x& = &10-9 \\\Leftrightarrow & -11x& = &1 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{1}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-1}{11} & & \\ & V = \left\{ \frac{-1}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (4x-2)& = & -5 \color{red}{-} (-12-5x) \\\Leftrightarrow & 8x-4& = &-5+12+5x \\\Leftrightarrow & 8x \color{red}{-4} & = &7 \color{red}{+5x} \\\Leftrightarrow & 8x \color{red}{-4} \color{blue}{+4} \color{blue}{-5x} & = &7 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+4} \\\Leftrightarrow & 8x-5x& = &7+4 \\\Leftrightarrow & 3x& = &11 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{11}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{11}{3} & & \\ & V = \left\{ \frac{11}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (4x-7)& = & 8 \color{red}{+} (12+x) \\\Leftrightarrow & 20x-35& = &8+12+x \\\Leftrightarrow & 20x \color{red}{-35} & = &20 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{-35} \color{blue}{+35} \color{blue}{-x} & = &20 \color{red}{+x} \color{blue}{-x} \color{blue}{+35} \\\Leftrightarrow & 20x-x& = &20+35 \\\Leftrightarrow & 19x& = &55 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{55}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{55}{19} & & \\ & V = \left\{ \frac{55}{19} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (x-6)& = & -15 \color{red}{-} (-13-5x) \\\Leftrightarrow & 6x-36& = &-15+13+5x \\\Leftrightarrow & 6x \color{red}{-36} & = &-2 \color{red}{+5x} \\\Leftrightarrow & 6x \color{red}{-36} \color{blue}{+36} \color{blue}{-5x} & = &-2 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+36} \\\Leftrightarrow & 6x-5x& = &-2+36 \\\Leftrightarrow & x& = &34 \\ & V = \left\{ 34 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (5x-5)& = & 9 \color{red}{-} (8+x) \\\Leftrightarrow & 25x-25& = &9-8-x \\\Leftrightarrow & 25x \color{red}{-25} & = &1 \color{red}{-x} \\\Leftrightarrow & 25x \color{red}{-25} \color{blue}{+25} \color{blue}{+x} & = &1 \color{red}{-x} \color{blue}{+x} \color{blue}{+25} \\\Leftrightarrow & 25x+x& = &1+25 \\\Leftrightarrow & 26x& = &26 \\\Leftrightarrow & \frac{26x}{ \color{red}{26} }& = &\frac{26}{ \color{red}{26} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (4x-6)& = & -15 \color{red}{+} (-11+x) \\\Leftrightarrow & 12x-18& = &-15-11+x \\\Leftrightarrow & 12x \color{red}{-18} & = &-26 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-18} \color{blue}{+18} \color{blue}{-x} & = &-26 \color{red}{+x} \color{blue}{-x} \color{blue}{+18} \\\Leftrightarrow & 12x-x& = &-26+18 \\\Leftrightarrow & 11x& = &-8 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-8}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-8}{11} & & \\ & V = \left\{ \frac{-8}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (-x+7)& = & -4 \color{red}{-} (10-4x) \\\Leftrightarrow & -5x+35& = &-4-10+4x \\\Leftrightarrow & -5x \color{red}{+35} & = &-14 \color{red}{+4x} \\\Leftrightarrow & -5x \color{red}{+35} \color{blue}{-35} \color{blue}{-4x} & = &-14 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-35} \\\Leftrightarrow & -5x-4x& = &-14-35 \\\Leftrightarrow & -9x& = &-49 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{-49}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{49}{9} & & \\ & V = \left\{ \frac{49}{9} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (-6x+4)& = & -13 \color{red}{-} (14-5x) \\\Leftrightarrow & -18x+12& = &-13-14+5x \\\Leftrightarrow & -18x \color{red}{+12} & = &-27 \color{red}{+5x} \\\Leftrightarrow & -18x \color{red}{+12} \color{blue}{-12} \color{blue}{-5x} & = &-27 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-12} \\\Leftrightarrow & -18x-5x& = &-27-12 \\\Leftrightarrow & -23x& = &-39 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-39}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{39}{23} & & \\ & V = \left\{ \frac{39}{23} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (x-3)& = & -2 \color{red}{-} (-8-4x) \\\Leftrightarrow & 5x-15& = &-2+8+4x \\\Leftrightarrow & 5x \color{red}{-15} & = &6 \color{red}{+4x} \\\Leftrightarrow & 5x \color{red}{-15} \color{blue}{+15} \color{blue}{-4x} & = &6 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+15} \\\Leftrightarrow & 5x-4x& = &6+15 \\\Leftrightarrow & x& = &21 \\ & V = \left\{ 21 \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (-x+4)& = & -11 \color{red}{-} (15+3x) \\\Leftrightarrow & -5x+20& = &-11-15-3x \\\Leftrightarrow & -5x \color{red}{+20} & = &-26 \color{red}{-3x} \\\Leftrightarrow & -5x \color{red}{+20} \color{blue}{-20} \color{blue}{+3x} & = &-26 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-20} \\\Leftrightarrow & -5x+3x& = &-26-20 \\\Leftrightarrow & -2x& = &-46 \\\Leftrightarrow & \frac{-2x}{ \color{red}{-2} }& = &\frac{-46}{ \color{red}{-2} } \\\Leftrightarrow & x = 23 & & \\ & V = \left\{ 23 \right\} & \\\end{align}\)