Vgln. eerste graad (reeks 3)

Hoofdmenu Eentje per keer  🖨

Reeks met haakjes

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

---

Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (3x+1)& = & 14 \color{red}{-} (13+x) \\\Leftrightarrow & 12x+4& = &14-13-x \\\Leftrightarrow & 12x \color{red}{+4} & = &1 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+4} \color{blue}{-4} \color{blue}{+x} & = &1 \color{red}{-x} \color{blue}{+x} \color{blue}{-4} \\\Leftrightarrow & 12x+x& = &1-4 \\\Leftrightarrow & 13x& = &-3 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-3}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-3}{13} & & \\ & V = \left\{ \frac{-3}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (-6x+7)& = & 4 \color{red}{+} (-7+x) \\\Leftrightarrow & -18x+21& = &4-7+x \\\Leftrightarrow & -18x \color{red}{+21} & = &-3 \color{red}{+x} \\\Leftrightarrow & -18x \color{red}{+21} \color{blue}{-21} \color{blue}{-x} & = &-3 \color{red}{+x} \color{blue}{-x} \color{blue}{-21} \\\Leftrightarrow & -18x-x& = &-3-21 \\\Leftrightarrow & -19x& = &-24 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-24}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{24}{19} & & \\ & V = \left\{ \frac{24}{19} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (-2x-2)& = & 8 \color{red}{-} (11+x) \\\Leftrightarrow & -6x-6& = &8-11-x \\\Leftrightarrow & -6x \color{red}{-6} & = &-3 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &-3 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & -6x+x& = &-3+6 \\\Leftrightarrow & -5x& = &3 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{3}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-3}{5} & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (x-7)& = & 5 \color{red}{+} (3+x) \\\Leftrightarrow & 3x-21& = &5+3+x \\\Leftrightarrow & 3x \color{red}{-21} & = &8 \color{red}{+x} \\\Leftrightarrow & 3x \color{red}{-21} \color{blue}{+21} \color{blue}{-x} & = &8 \color{red}{+x} \color{blue}{-x} \color{blue}{+21} \\\Leftrightarrow & 3x-x& = &8+21 \\\Leftrightarrow & 2x& = &29 \\\Leftrightarrow & \frac{2x}{ \color{red}{2} }& = &\frac{29}{ \color{red}{2} } \\\Leftrightarrow & x = \frac{29}{2} & & \\ & V = \left\{ \frac{29}{2} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (-5x-2)& = & 11 \color{red}{+} (-12+3x) \\\Leftrightarrow & -25x-10& = &11-12+3x \\\Leftrightarrow & -25x \color{red}{-10} & = &-1 \color{red}{+3x} \\\Leftrightarrow & -25x \color{red}{-10} \color{blue}{+10} \color{blue}{-3x} & = &-1 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+10} \\\Leftrightarrow & -25x-3x& = &-1+10 \\\Leftrightarrow & -28x& = &9 \\\Leftrightarrow & \frac{-28x}{ \color{red}{-28} }& = &\frac{9}{ \color{red}{-28} } \\\Leftrightarrow & x = \frac{-9}{28} & & \\ & V = \left\{ \frac{-9}{28} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (x+7)& = & -14 \color{red}{+} (-5-5x) \\\Leftrightarrow & 6x+42& = &-14-5-5x \\\Leftrightarrow & 6x \color{red}{+42} & = &-19 \color{red}{-5x} \\\Leftrightarrow & 6x \color{red}{+42} \color{blue}{-42} \color{blue}{+5x} & = &-19 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-42} \\\Leftrightarrow & 6x+5x& = &-19-42 \\\Leftrightarrow & 11x& = &-61 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-61}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-61}{11} & & \\ & V = \left\{ \frac{-61}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (5x-5)& = & 13 \color{red}{+} (-15-3x) \\\Leftrightarrow & 10x-10& = &13-15-3x \\\Leftrightarrow & 10x \color{red}{-10} & = &-2 \color{red}{-3x} \\\Leftrightarrow & 10x \color{red}{-10} \color{blue}{+10} \color{blue}{+3x} & = &-2 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+10} \\\Leftrightarrow & 10x+3x& = &-2+10 \\\Leftrightarrow & 13x& = &8 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{8}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{8}{13} & & \\ & V = \left\{ \frac{8}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (2x+6)& = & -2 \color{red}{+} (-8+x) \\\Leftrightarrow & 6x+18& = &-2-8+x \\\Leftrightarrow & 6x \color{red}{+18} & = &-10 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{+18} \color{blue}{-18} \color{blue}{-x} & = &-10 \color{red}{+x} \color{blue}{-x} \color{blue}{-18} \\\Leftrightarrow & 6x-x& = &-10-18 \\\Leftrightarrow & 5x& = &-28 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-28}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{-28}{5} & & \\ & V = \left\{ \frac{-28}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (x+2)& = & 12 \color{red}{+} (-14+x) \\\Leftrightarrow & 6x+12& = &12-14+x \\\Leftrightarrow & 6x \color{red}{+12} & = &-2 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &-2 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & 6x-x& = &-2-12 \\\Leftrightarrow & 5x& = &-14 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-14}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{-14}{5} & & \\ & V = \left\{ \frac{-14}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (x-2)& = & 10 \color{red}{+} (-10-5x) \\\Leftrightarrow & 3x-6& = &10-10-5x \\\Leftrightarrow & 3x \color{red}{-6} & = &0 \color{red}{-5x} \\\Leftrightarrow & 3x \color{red}{-6} \color{blue}{+6} \color{blue}{+5x} & = &0 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+6} \\\Leftrightarrow & 3x+5x& = &0+6 \\\Leftrightarrow & 8x& = &6 \\\Leftrightarrow & \frac{8x}{ \color{red}{8} }& = &\frac{6}{ \color{red}{8} } \\\Leftrightarrow & x = \frac{3}{4} & & \\ & V = \left\{ \frac{3}{4} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (-3x+1)& = & -6 \color{red}{-} (7+x) \\\Leftrightarrow & -12x+4& = &-6-7-x \\\Leftrightarrow & -12x \color{red}{+4} & = &-13 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+4} \color{blue}{-4} \color{blue}{+x} & = &-13 \color{red}{-x} \color{blue}{+x} \color{blue}{-4} \\\Leftrightarrow & -12x+x& = &-13-4 \\\Leftrightarrow & -11x& = &-17 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-17}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{17}{11} & & \\ & V = \left\{ \frac{17}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (-4x-2)& = & 7 \color{red}{+} (-13+x) \\\Leftrightarrow & -16x-8& = &7-13+x \\\Leftrightarrow & -16x \color{red}{-8} & = &-6 \color{red}{+x} \\\Leftrightarrow & -16x \color{red}{-8} \color{blue}{+8} \color{blue}{-x} & = &-6 \color{red}{+x} \color{blue}{-x} \color{blue}{+8} \\\Leftrightarrow & -16x-x& = &-6+8 \\\Leftrightarrow & -17x& = &2 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{2}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{-2}{17} & & \\ & V = \left\{ \frac{-2}{17} \right\} & \\\end{align}\)