Vgln. eerste graad (reeks 3)

Hoofdmenu Eentje per keer  🖨

Reeks met haakjes

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

---

Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (6x+4)& = & 15 \color{red}{-} (-1+x) \\\Leftrightarrow & 18x+12& = &15+1-x \\\Leftrightarrow & 18x \color{red}{+12} & = &16 \color{red}{-x} \\\Leftrightarrow & 18x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &16 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & 18x+x& = &16-12 \\\Leftrightarrow & 19x& = &4 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{4}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{4}{19} & & \\ & V = \left\{ \frac{4}{19} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (-5x-2)& = & -8 \color{red}{+} (-1-2x) \\\Leftrightarrow & -25x-10& = &-8-1-2x \\\Leftrightarrow & -25x \color{red}{-10} & = &-9 \color{red}{-2x} \\\Leftrightarrow & -25x \color{red}{-10} \color{blue}{+10} \color{blue}{+2x} & = &-9 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+10} \\\Leftrightarrow & -25x+2x& = &-9+10 \\\Leftrightarrow & -23x& = &1 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{1}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-1}{23} & & \\ & V = \left\{ \frac{-1}{23} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (x+7)& = & 7 \color{red}{-} (4+x) \\\Leftrightarrow & 6x+42& = &7-4-x \\\Leftrightarrow & 6x \color{red}{+42} & = &3 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{+42} \color{blue}{-42} \color{blue}{+x} & = &3 \color{red}{-x} \color{blue}{+x} \color{blue}{-42} \\\Leftrightarrow & 6x+x& = &3-42 \\\Leftrightarrow & 7x& = &-39 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-39}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-39}{7} & & \\ & V = \left\{ \frac{-39}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (3x-2)& = & 6 \color{red}{-} (6+x) \\\Leftrightarrow & 12x-8& = &6-6-x \\\Leftrightarrow & 12x \color{red}{-8} & = &0 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-8} \color{blue}{+8} \color{blue}{+x} & = &0 \color{red}{-x} \color{blue}{+x} \color{blue}{+8} \\\Leftrightarrow & 12x+x& = &0+8 \\\Leftrightarrow & 13x& = &8 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{8}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{8}{13} & & \\ & V = \left\{ \frac{8}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (x+4)& = & -2 \color{red}{-} (-12-5x) \\\Leftrightarrow & 6x+24& = &-2+12+5x \\\Leftrightarrow & 6x \color{red}{+24} & = &10 \color{red}{+5x} \\\Leftrightarrow & 6x \color{red}{+24} \color{blue}{-24} \color{blue}{-5x} & = &10 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-24} \\\Leftrightarrow & 6x-5x& = &10-24 \\\Leftrightarrow & x& = &-14 \\ & V = \left\{ -14 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (x-1)& = & 6 \color{red}{-} (-13+x) \\\Leftrightarrow & 4x-4& = &6+13-x \\\Leftrightarrow & 4x \color{red}{-4} & = &19 \color{red}{-x} \\\Leftrightarrow & 4x \color{red}{-4} \color{blue}{+4} \color{blue}{+x} & = &19 \color{red}{-x} \color{blue}{+x} \color{blue}{+4} \\\Leftrightarrow & 4x+x& = &19+4 \\\Leftrightarrow & 5x& = &23 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{23}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{23}{5} & & \\ & V = \left\{ \frac{23}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (3x-4)& = & 15 \color{red}{+} (5+4x) \\\Leftrightarrow & 15x-20& = &15+5+4x \\\Leftrightarrow & 15x \color{red}{-20} & = &20 \color{red}{+4x} \\\Leftrightarrow & 15x \color{red}{-20} \color{blue}{+20} \color{blue}{-4x} & = &20 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+20} \\\Leftrightarrow & 15x-4x& = &20+20 \\\Leftrightarrow & 11x& = &40 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{40}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{40}{11} & & \\ & V = \left\{ \frac{40}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (-x-1)& = & -13 \color{red}{-} (-7-5x) \\\Leftrightarrow & -3x-3& = &-13+7+5x \\\Leftrightarrow & -3x \color{red}{-3} & = &-6 \color{red}{+5x} \\\Leftrightarrow & -3x \color{red}{-3} \color{blue}{+3} \color{blue}{-5x} & = &-6 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+3} \\\Leftrightarrow & -3x-5x& = &-6+3 \\\Leftrightarrow & -8x& = &-3 \\\Leftrightarrow & \frac{-8x}{ \color{red}{-8} }& = &\frac{-3}{ \color{red}{-8} } \\\Leftrightarrow & x = \frac{3}{8} & & \\ & V = \left\{ \frac{3}{8} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (5x+7)& = & -15 \color{red}{-} (11+x) \\\Leftrightarrow & 25x+35& = &-15-11-x \\\Leftrightarrow & 25x \color{red}{+35} & = &-26 \color{red}{-x} \\\Leftrightarrow & 25x \color{red}{+35} \color{blue}{-35} \color{blue}{+x} & = &-26 \color{red}{-x} \color{blue}{+x} \color{blue}{-35} \\\Leftrightarrow & 25x+x& = &-26-35 \\\Leftrightarrow & 26x& = &-61 \\\Leftrightarrow & \frac{26x}{ \color{red}{26} }& = &\frac{-61}{ \color{red}{26} } \\\Leftrightarrow & x = \frac{-61}{26} & & \\ & V = \left\{ \frac{-61}{26} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (-x-2)& = & -14 \color{red}{-} (5+x) \\\Leftrightarrow & -3x-6& = &-14-5-x \\\Leftrightarrow & -3x \color{red}{-6} & = &-19 \color{red}{-x} \\\Leftrightarrow & -3x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &-19 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & -3x+x& = &-19+6 \\\Leftrightarrow & -2x& = &-13 \\\Leftrightarrow & \frac{-2x}{ \color{red}{-2} }& = &\frac{-13}{ \color{red}{-2} } \\\Leftrightarrow & x = \frac{13}{2} & & \\ & V = \left\{ \frac{13}{2} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (-4x+4)& = & 11 \color{red}{-} (2-5x) \\\Leftrightarrow & -8x+8& = &11-2+5x \\\Leftrightarrow & -8x \color{red}{+8} & = &9 \color{red}{+5x} \\\Leftrightarrow & -8x \color{red}{+8} \color{blue}{-8} \color{blue}{-5x} & = &9 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-8} \\\Leftrightarrow & -8x-5x& = &9-8 \\\Leftrightarrow & -13x& = &1 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{1}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-1}{13} & & \\ & V = \left\{ \frac{-1}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (2x+7)& = & -10 \color{red}{-} (-3+3x) \\\Leftrightarrow & 8x+28& = &-10+3-3x \\\Leftrightarrow & 8x \color{red}{+28} & = &-7 \color{red}{-3x} \\\Leftrightarrow & 8x \color{red}{+28} \color{blue}{-28} \color{blue}{+3x} & = &-7 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-28} \\\Leftrightarrow & 8x+3x& = &-7-28 \\\Leftrightarrow & 11x& = &-35 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-35}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-35}{11} & & \\ & V = \left\{ \frac{-35}{11} \right\} & \\\end{align}\)