Vgln. eerste graad (reeks 3)

Hoofdmenu Eentje per keer  🖨

Reeks met haakjes

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

---

Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (2x+7)& = & -4 \color{red}{+} (14+3x) \\\Leftrightarrow & 10x+35& = &-4+14+3x \\\Leftrightarrow & 10x \color{red}{+35} & = &10 \color{red}{+3x} \\\Leftrightarrow & 10x \color{red}{+35} \color{blue}{-35} \color{blue}{-3x} & = &10 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-35} \\\Leftrightarrow & 10x-3x& = &10-35 \\\Leftrightarrow & 7x& = &-25 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-25}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-25}{7} & & \\ & V = \left\{ \frac{-25}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (6x-6)& = & -15 \color{red}{-} (15+x) \\\Leftrightarrow & 30x-30& = &-15-15-x \\\Leftrightarrow & 30x \color{red}{-30} & = &-30 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{-30} \color{blue}{+30} \color{blue}{+x} & = &-30 \color{red}{-x} \color{blue}{+x} \color{blue}{+30} \\\Leftrightarrow & 30x+x& = &-30+30 \\\Leftrightarrow & 31x& = &0 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{0}{ \color{red}{31} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (-3x-5)& = & 7 \color{red}{+} (-3+2x) \\\Leftrightarrow & -9x-15& = &7-3+2x \\\Leftrightarrow & -9x \color{red}{-15} & = &4 \color{red}{+2x} \\\Leftrightarrow & -9x \color{red}{-15} \color{blue}{+15} \color{blue}{-2x} & = &4 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+15} \\\Leftrightarrow & -9x-2x& = &4+15 \\\Leftrightarrow & -11x& = &19 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{19}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-19}{11} & & \\ & V = \left\{ \frac{-19}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (-4x-2)& = & -2 \color{red}{-} (7+x) \\\Leftrightarrow & -24x-12& = &-2-7-x \\\Leftrightarrow & -24x \color{red}{-12} & = &-9 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &-9 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & -24x+x& = &-9+12 \\\Leftrightarrow & -23x& = &3 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{3}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-3}{23} & & \\ & V = \left\{ \frac{-3}{23} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (-x-2)& = & 8 \color{red}{-} (-12-3x) \\\Leftrightarrow & -4x-8& = &8+12+3x \\\Leftrightarrow & -4x \color{red}{-8} & = &20 \color{red}{+3x} \\\Leftrightarrow & -4x \color{red}{-8} \color{blue}{+8} \color{blue}{-3x} & = &20 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+8} \\\Leftrightarrow & -4x-3x& = &20+8 \\\Leftrightarrow & -7x& = &28 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{28}{ \color{red}{-7} } \\\Leftrightarrow & x = -4 & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (6x+1)& = & -4 \color{red}{-} (-15+x) \\\Leftrightarrow & 36x+6& = &-4+15-x \\\Leftrightarrow & 36x \color{red}{+6} & = &11 \color{red}{-x} \\\Leftrightarrow & 36x \color{red}{+6} \color{blue}{-6} \color{blue}{+x} & = &11 \color{red}{-x} \color{blue}{+x} \color{blue}{-6} \\\Leftrightarrow & 36x+x& = &11-6 \\\Leftrightarrow & 37x& = &5 \\\Leftrightarrow & \frac{37x}{ \color{red}{37} }& = &\frac{5}{ \color{red}{37} } \\\Leftrightarrow & x = \frac{5}{37} & & \\ & V = \left\{ \frac{5}{37} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (x+6)& = & -7 \color{red}{+} (12+3x) \\\Leftrightarrow & 2x+12& = &-7+12+3x \\\Leftrightarrow & 2x \color{red}{+12} & = &5 \color{red}{+3x} \\\Leftrightarrow & 2x \color{red}{+12} \color{blue}{-12} \color{blue}{-3x} & = &5 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-12} \\\Leftrightarrow & 2x-3x& = &5-12 \\\Leftrightarrow & -x& = &-7 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-7}{ \color{red}{-1} } \\\Leftrightarrow & x = 7 & & \\ & V = \left\{ 7 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (-x+4)& = & 13 \color{red}{+} (5+x) \\\Leftrightarrow & -6x+24& = &13+5+x \\\Leftrightarrow & -6x \color{red}{+24} & = &18 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{+24} \color{blue}{-24} \color{blue}{-x} & = &18 \color{red}{+x} \color{blue}{-x} \color{blue}{-24} \\\Leftrightarrow & -6x-x& = &18-24 \\\Leftrightarrow & -7x& = &-6 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-6}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{6}{7} & & \\ & V = \left\{ \frac{6}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (-x-4)& = & 7 \color{red}{-} (-15+x) \\\Leftrightarrow & -2x-8& = &7+15-x \\\Leftrightarrow & -2x \color{red}{-8} & = &22 \color{red}{-x} \\\Leftrightarrow & -2x \color{red}{-8} \color{blue}{+8} \color{blue}{+x} & = &22 \color{red}{-x} \color{blue}{+x} \color{blue}{+8} \\\Leftrightarrow & -2x+x& = &22+8 \\\Leftrightarrow & -x& = &30 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{30}{ \color{red}{-1} } \\\Leftrightarrow & x = -30 & & \\ & V = \left\{ -30 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (5x-2)& = & 7 \color{red}{+} (7+x) \\\Leftrightarrow & 20x-8& = &7+7+x \\\Leftrightarrow & 20x \color{red}{-8} & = &14 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{-8} \color{blue}{+8} \color{blue}{-x} & = &14 \color{red}{+x} \color{blue}{-x} \color{blue}{+8} \\\Leftrightarrow & 20x-x& = &14+8 \\\Leftrightarrow & 19x& = &22 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{22}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{22}{19} & & \\ & V = \left\{ \frac{22}{19} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (-6x+4)& = & -5 \color{red}{+} (2+x) \\\Leftrightarrow & -12x+8& = &-5+2+x \\\Leftrightarrow & -12x \color{red}{+8} & = &-3 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+8} \color{blue}{-8} \color{blue}{-x} & = &-3 \color{red}{+x} \color{blue}{-x} \color{blue}{-8} \\\Leftrightarrow & -12x-x& = &-3-8 \\\Leftrightarrow & -13x& = &-11 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-11}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{11}{13} & & \\ & V = \left\{ \frac{11}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (5x-5)& = & 10 \color{red}{-} (13+x) \\\Leftrightarrow & 30x-30& = &10-13-x \\\Leftrightarrow & 30x \color{red}{-30} & = &-3 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{-30} \color{blue}{+30} \color{blue}{+x} & = &-3 \color{red}{-x} \color{blue}{+x} \color{blue}{+30} \\\Leftrightarrow & 30x+x& = &-3+30 \\\Leftrightarrow & 31x& = &27 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{27}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{27}{31} & & \\ & V = \left\{ \frac{27}{31} \right\} & \\\end{align}\)