Vgln. eerste graad (reeks 3)

Hoofdmenu Eentje per keer  🖨

Reeks met haakjes

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

---

Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (x-1)& = & 10 \color{red}{+} (-1+2x) \\\Leftrightarrow & 3x-3& = &10-1+2x \\\Leftrightarrow & 3x \color{red}{-3} & = &9 \color{red}{+2x} \\\Leftrightarrow & 3x \color{red}{-3} \color{blue}{+3} \color{blue}{-2x} & = &9 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+3} \\\Leftrightarrow & 3x-2x& = &9+3 \\\Leftrightarrow & x& = &12 \\ & V = \left\{ 12 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (-6x+2)& = & 15 \color{red}{-} (-9+x) \\\Leftrightarrow & -30x+10& = &15+9-x \\\Leftrightarrow & -30x \color{red}{+10} & = &24 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{+10} \color{blue}{-10} \color{blue}{+x} & = &24 \color{red}{-x} \color{blue}{+x} \color{blue}{-10} \\\Leftrightarrow & -30x+x& = &24-10 \\\Leftrightarrow & -29x& = &14 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{14}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{-14}{29} & & \\ & V = \left\{ \frac{-14}{29} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (-4x+7)& = & 2 \color{red}{+} (-2+x) \\\Leftrightarrow & -20x+35& = &2-2+x \\\Leftrightarrow & -20x \color{red}{+35} & = &0 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{+35} \color{blue}{-35} \color{blue}{-x} & = &0 \color{red}{+x} \color{blue}{-x} \color{blue}{-35} \\\Leftrightarrow & -20x-x& = &0-35 \\\Leftrightarrow & -21x& = &-35 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{-35}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{5}{3} & & \\ & V = \left\{ \frac{5}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (5x+6)& = & -3 \color{red}{+} (-13+x) \\\Leftrightarrow & 20x+24& = &-3-13+x \\\Leftrightarrow & 20x \color{red}{+24} & = &-16 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{+24} \color{blue}{-24} \color{blue}{-x} & = &-16 \color{red}{+x} \color{blue}{-x} \color{blue}{-24} \\\Leftrightarrow & 20x-x& = &-16-24 \\\Leftrightarrow & 19x& = &-40 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-40}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-40}{19} & & \\ & V = \left\{ \frac{-40}{19} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (4x-1)& = & -3 \color{red}{+} (-15+x) \\\Leftrightarrow & 20x-5& = &-3-15+x \\\Leftrightarrow & 20x \color{red}{-5} & = &-18 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{-5} \color{blue}{+5} \color{blue}{-x} & = &-18 \color{red}{+x} \color{blue}{-x} \color{blue}{+5} \\\Leftrightarrow & 20x-x& = &-18+5 \\\Leftrightarrow & 19x& = &-13 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-13}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-13}{19} & & \\ & V = \left\{ \frac{-13}{19} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (6x+3)& = & -2 \color{red}{+} (-11+x) \\\Leftrightarrow & 24x+12& = &-2-11+x \\\Leftrightarrow & 24x \color{red}{+12} & = &-13 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &-13 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & 24x-x& = &-13-12 \\\Leftrightarrow & 23x& = &-25 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-25}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-25}{23} & & \\ & V = \left\{ \frac{-25}{23} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (6x+1)& = & -3 \color{red}{-} (-11+x) \\\Leftrightarrow & 36x+6& = &-3+11-x \\\Leftrightarrow & 36x \color{red}{+6} & = &8 \color{red}{-x} \\\Leftrightarrow & 36x \color{red}{+6} \color{blue}{-6} \color{blue}{+x} & = &8 \color{red}{-x} \color{blue}{+x} \color{blue}{-6} \\\Leftrightarrow & 36x+x& = &8-6 \\\Leftrightarrow & 37x& = &2 \\\Leftrightarrow & \frac{37x}{ \color{red}{37} }& = &\frac{2}{ \color{red}{37} } \\\Leftrightarrow & x = \frac{2}{37} & & \\ & V = \left\{ \frac{2}{37} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (-3x-4)& = & 6 \color{red}{-} (13-5x) \\\Leftrightarrow & -6x-8& = &6-13+5x \\\Leftrightarrow & -6x \color{red}{-8} & = &-7 \color{red}{+5x} \\\Leftrightarrow & -6x \color{red}{-8} \color{blue}{+8} \color{blue}{-5x} & = &-7 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+8} \\\Leftrightarrow & -6x-5x& = &-7+8 \\\Leftrightarrow & -11x& = &1 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{1}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-1}{11} & & \\ & V = \left\{ \frac{-1}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (-2x+3)& = & -6 \color{red}{-} (-12-3x) \\\Leftrightarrow & -4x+6& = &-6+12+3x \\\Leftrightarrow & -4x \color{red}{+6} & = &6 \color{red}{+3x} \\\Leftrightarrow & -4x \color{red}{+6} \color{blue}{-6} \color{blue}{-3x} & = &6 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-6} \\\Leftrightarrow & -4x-3x& = &6-6 \\\Leftrightarrow & -7x& = &0 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{0}{ \color{red}{-7} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (-4x+3)& = & -6 \color{red}{+} (7+x) \\\Leftrightarrow & -24x+18& = &-6+7+x \\\Leftrightarrow & -24x \color{red}{+18} & = &1 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{+18} \color{blue}{-18} \color{blue}{-x} & = &1 \color{red}{+x} \color{blue}{-x} \color{blue}{-18} \\\Leftrightarrow & -24x-x& = &1-18 \\\Leftrightarrow & -25x& = &-17 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{-17}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{17}{25} & & \\ & V = \left\{ \frac{17}{25} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (x-7)& = & 6 \color{red}{-} (10+x) \\\Leftrightarrow & 6x-42& = &6-10-x \\\Leftrightarrow & 6x \color{red}{-42} & = &-4 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{-42} \color{blue}{+42} \color{blue}{+x} & = &-4 \color{red}{-x} \color{blue}{+x} \color{blue}{+42} \\\Leftrightarrow & 6x+x& = &-4+42 \\\Leftrightarrow & 7x& = &38 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{38}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{38}{7} & & \\ & V = \left\{ \frac{38}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (-4x-2)& = & 12 \color{red}{-} (1+3x) \\\Leftrightarrow & -16x-8& = &12-1-3x \\\Leftrightarrow & -16x \color{red}{-8} & = &11 \color{red}{-3x} \\\Leftrightarrow & -16x \color{red}{-8} \color{blue}{+8} \color{blue}{+3x} & = &11 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+8} \\\Leftrightarrow & -16x+3x& = &11+8 \\\Leftrightarrow & -13x& = &19 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{19}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-19}{13} & & \\ & V = \left\{ \frac{-19}{13} \right\} & \\\end{align}\)