Vgln. eerste graad (reeks 3)

Hoofdmenu Eentje per keer  🖨

Reeks met haakjes

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

---

Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (6x+2)& = & 2 \color{red}{-} (-6+x) \\\Leftrightarrow & 30x+10& = &2+6-x \\\Leftrightarrow & 30x \color{red}{+10} & = &8 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{+10} \color{blue}{-10} \color{blue}{+x} & = &8 \color{red}{-x} \color{blue}{+x} \color{blue}{-10} \\\Leftrightarrow & 30x+x& = &8-10 \\\Leftrightarrow & 31x& = &-2 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{-2}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{-2}{31} & & \\ & V = \left\{ \frac{-2}{31} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (-x-4)& = & 2 \color{red}{-} (-13-2x) \\\Leftrightarrow & -3x-12& = &2+13+2x \\\Leftrightarrow & -3x \color{red}{-12} & = &15 \color{red}{+2x} \\\Leftrightarrow & -3x \color{red}{-12} \color{blue}{+12} \color{blue}{-2x} & = &15 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+12} \\\Leftrightarrow & -3x-2x& = &15+12 \\\Leftrightarrow & -5x& = &27 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{27}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-27}{5} & & \\ & V = \left\{ \frac{-27}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (-2x+5)& = & 6 \color{red}{+} (13-3x) \\\Leftrightarrow & -4x+10& = &6+13-3x \\\Leftrightarrow & -4x \color{red}{+10} & = &19 \color{red}{-3x} \\\Leftrightarrow & -4x \color{red}{+10} \color{blue}{-10} \color{blue}{+3x} & = &19 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-10} \\\Leftrightarrow & -4x+3x& = &19-10 \\\Leftrightarrow & -x& = &9 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{9}{ \color{red}{-1} } \\\Leftrightarrow & x = -9 & & \\ & V = \left\{ -9 \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (-5x-1)& = & 4 \color{red}{+} (2+x) \\\Leftrightarrow & -30x-6& = &4+2+x \\\Leftrightarrow & -30x \color{red}{-6} & = &6 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &6 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & -30x-x& = &6+6 \\\Leftrightarrow & -31x& = &12 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{12}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{-12}{31} & & \\ & V = \left\{ \frac{-12}{31} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (3x-1)& = & 7 \color{red}{-} (-3-2x) \\\Leftrightarrow & 15x-5& = &7+3+2x \\\Leftrightarrow & 15x \color{red}{-5} & = &10 \color{red}{+2x} \\\Leftrightarrow & 15x \color{red}{-5} \color{blue}{+5} \color{blue}{-2x} & = &10 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+5} \\\Leftrightarrow & 15x-2x& = &10+5 \\\Leftrightarrow & 13x& = &15 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{15}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{15}{13} & & \\ & V = \left\{ \frac{15}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (-4x+7)& = & -3 \color{red}{-} (11+x) \\\Leftrightarrow & -24x+42& = &-3-11-x \\\Leftrightarrow & -24x \color{red}{+42} & = &-14 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{+42} \color{blue}{-42} \color{blue}{+x} & = &-14 \color{red}{-x} \color{blue}{+x} \color{blue}{-42} \\\Leftrightarrow & -24x+x& = &-14-42 \\\Leftrightarrow & -23x& = &-56 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-56}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{56}{23} & & \\ & V = \left\{ \frac{56}{23} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (-2x+2)& = & -1 \color{red}{-} (8+3x) \\\Leftrightarrow & -8x+8& = &-1-8-3x \\\Leftrightarrow & -8x \color{red}{+8} & = &-9 \color{red}{-3x} \\\Leftrightarrow & -8x \color{red}{+8} \color{blue}{-8} \color{blue}{+3x} & = &-9 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-8} \\\Leftrightarrow & -8x+3x& = &-9-8 \\\Leftrightarrow & -5x& = &-17 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-17}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{17}{5} & & \\ & V = \left\{ \frac{17}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (x+2)& = & -10 \color{red}{+} (-2-2x) \\\Leftrightarrow & 3x+6& = &-10-2-2x \\\Leftrightarrow & 3x \color{red}{+6} & = &-12 \color{red}{-2x} \\\Leftrightarrow & 3x \color{red}{+6} \color{blue}{-6} \color{blue}{+2x} & = &-12 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-6} \\\Leftrightarrow & 3x+2x& = &-12-6 \\\Leftrightarrow & 5x& = &-18 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-18}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{-18}{5} & & \\ & V = \left\{ \frac{-18}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (5x+5)& = & -11 \color{red}{+} (15-4x) \\\Leftrightarrow & 25x+25& = &-11+15-4x \\\Leftrightarrow & 25x \color{red}{+25} & = &4 \color{red}{-4x} \\\Leftrightarrow & 25x \color{red}{+25} \color{blue}{-25} \color{blue}{+4x} & = &4 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-25} \\\Leftrightarrow & 25x+4x& = &4-25 \\\Leftrightarrow & 29x& = &-21 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{-21}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{-21}{29} & & \\ & V = \left\{ \frac{-21}{29} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (3x+3)& = & -2 \color{red}{-} (2-5x) \\\Leftrightarrow & 18x+18& = &-2-2+5x \\\Leftrightarrow & 18x \color{red}{+18} & = &-4 \color{red}{+5x} \\\Leftrightarrow & 18x \color{red}{+18} \color{blue}{-18} \color{blue}{-5x} & = &-4 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-18} \\\Leftrightarrow & 18x-5x& = &-4-18 \\\Leftrightarrow & 13x& = &-22 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-22}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-22}{13} & & \\ & V = \left\{ \frac{-22}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (-3x+4)& = & -5 \color{red}{-} (9+x) \\\Leftrightarrow & -12x+16& = &-5-9-x \\\Leftrightarrow & -12x \color{red}{+16} & = &-14 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+16} \color{blue}{-16} \color{blue}{+x} & = &-14 \color{red}{-x} \color{blue}{+x} \color{blue}{-16} \\\Leftrightarrow & -12x+x& = &-14-16 \\\Leftrightarrow & -11x& = &-30 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-30}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{30}{11} & & \\ & V = \left\{ \frac{30}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (6x-3)& = & 6 \color{red}{+} (-5-5x) \\\Leftrightarrow & 18x-9& = &6-5-5x \\\Leftrightarrow & 18x \color{red}{-9} & = &1 \color{red}{-5x} \\\Leftrightarrow & 18x \color{red}{-9} \color{blue}{+9} \color{blue}{+5x} & = &1 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+9} \\\Leftrightarrow & 18x+5x& = &1+9 \\\Leftrightarrow & 23x& = &10 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{10}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{10}{23} & & \\ & V = \left\{ \frac{10}{23} \right\} & \\\end{align}\)