Vgln. eerste graad (reeks 3)

Hoofdmenu Eentje per keer  🖨

Reeks met haakjes

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

---

Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (-3x+6)& = & 9 \color{red}{-} (-12+x) \\\Leftrightarrow & -12x+24& = &9+12-x \\\Leftrightarrow & -12x \color{red}{+24} & = &21 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+24} \color{blue}{-24} \color{blue}{+x} & = &21 \color{red}{-x} \color{blue}{+x} \color{blue}{-24} \\\Leftrightarrow & -12x+x& = &21-24 \\\Leftrightarrow & -11x& = &-3 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-3}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{3}{11} & & \\ & V = \left\{ \frac{3}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (-4x-1)& = & 4 \color{red}{+} (4+x) \\\Leftrightarrow & -20x-5& = &4+4+x \\\Leftrightarrow & -20x \color{red}{-5} & = &8 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{-5} \color{blue}{+5} \color{blue}{-x} & = &8 \color{red}{+x} \color{blue}{-x} \color{blue}{+5} \\\Leftrightarrow & -20x-x& = &8+5 \\\Leftrightarrow & -21x& = &13 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{13}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{-13}{21} & & \\ & V = \left\{ \frac{-13}{21} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (-3x-2)& = & -11 \color{red}{-} (1+x) \\\Leftrightarrow & -6x-4& = &-11-1-x \\\Leftrightarrow & -6x \color{red}{-4} & = &-12 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{-4} \color{blue}{+4} \color{blue}{+x} & = &-12 \color{red}{-x} \color{blue}{+x} \color{blue}{+4} \\\Leftrightarrow & -6x+x& = &-12+4 \\\Leftrightarrow & -5x& = &-8 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-8}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{8}{5} & & \\ & V = \left\{ \frac{8}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (-3x-1)& = & 13 \color{red}{+} (1+2x) \\\Leftrightarrow & -15x-5& = &13+1+2x \\\Leftrightarrow & -15x \color{red}{-5} & = &14 \color{red}{+2x} \\\Leftrightarrow & -15x \color{red}{-5} \color{blue}{+5} \color{blue}{-2x} & = &14 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+5} \\\Leftrightarrow & -15x-2x& = &14+5 \\\Leftrightarrow & -17x& = &19 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{19}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{-19}{17} & & \\ & V = \left\{ \frac{-19}{17} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (-6x-5)& = & -10 \color{red}{-} (12+x) \\\Leftrightarrow & -30x-25& = &-10-12-x \\\Leftrightarrow & -30x \color{red}{-25} & = &-22 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{-25} \color{blue}{+25} \color{blue}{+x} & = &-22 \color{red}{-x} \color{blue}{+x} \color{blue}{+25} \\\Leftrightarrow & -30x+x& = &-22+25 \\\Leftrightarrow & -29x& = &3 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{3}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{-3}{29} & & \\ & V = \left\{ \frac{-3}{29} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (-2x-2)& = & 12 \color{red}{-} (5+3x) \\\Leftrightarrow & -10x-10& = &12-5-3x \\\Leftrightarrow & -10x \color{red}{-10} & = &7 \color{red}{-3x} \\\Leftrightarrow & -10x \color{red}{-10} \color{blue}{+10} \color{blue}{+3x} & = &7 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+10} \\\Leftrightarrow & -10x+3x& = &7+10 \\\Leftrightarrow & -7x& = &17 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{17}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-17}{7} & & \\ & V = \left\{ \frac{-17}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (3x-4)& = & 2 \color{red}{-} (14-2x) \\\Leftrightarrow & 9x-12& = &2-14+2x \\\Leftrightarrow & 9x \color{red}{-12} & = &-12 \color{red}{+2x} \\\Leftrightarrow & 9x \color{red}{-12} \color{blue}{+12} \color{blue}{-2x} & = &-12 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+12} \\\Leftrightarrow & 9x-2x& = &-12+12 \\\Leftrightarrow & 7x& = &0 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{0}{ \color{red}{7} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (-5x-1)& = & 6 \color{red}{+} (10+x) \\\Leftrightarrow & -30x-6& = &6+10+x \\\Leftrightarrow & -30x \color{red}{-6} & = &16 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &16 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & -30x-x& = &16+6 \\\Leftrightarrow & -31x& = &22 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{22}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{-22}{31} & & \\ & V = \left\{ \frac{-22}{31} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (2x+6)& = & 6 \color{red}{-} (-6+x) \\\Leftrightarrow & 6x+18& = &6+6-x \\\Leftrightarrow & 6x \color{red}{+18} & = &12 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{+18} \color{blue}{-18} \color{blue}{+x} & = &12 \color{red}{-x} \color{blue}{+x} \color{blue}{-18} \\\Leftrightarrow & 6x+x& = &12-18 \\\Leftrightarrow & 7x& = &-6 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-6}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-6}{7} & & \\ & V = \left\{ \frac{-6}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (-4x-6)& = & 13 \color{red}{-} (-1+3x) \\\Leftrightarrow & -16x-24& = &13+1-3x \\\Leftrightarrow & -16x \color{red}{-24} & = &14 \color{red}{-3x} \\\Leftrightarrow & -16x \color{red}{-24} \color{blue}{+24} \color{blue}{+3x} & = &14 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+24} \\\Leftrightarrow & -16x+3x& = &14+24 \\\Leftrightarrow & -13x& = &38 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{38}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-38}{13} & & \\ & V = \left\{ \frac{-38}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (3x-7)& = & 1 \color{red}{-} (11+x) \\\Leftrightarrow & 15x-35& = &1-11-x \\\Leftrightarrow & 15x \color{red}{-35} & = &-10 \color{red}{-x} \\\Leftrightarrow & 15x \color{red}{-35} \color{blue}{+35} \color{blue}{+x} & = &-10 \color{red}{-x} \color{blue}{+x} \color{blue}{+35} \\\Leftrightarrow & 15x+x& = &-10+35 \\\Leftrightarrow & 16x& = &25 \\\Leftrightarrow & \frac{16x}{ \color{red}{16} }& = &\frac{25}{ \color{red}{16} } \\\Leftrightarrow & x = \frac{25}{16} & & \\ & V = \left\{ \frac{25}{16} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (x+2)& = & 14 \color{red}{-} (-14-3x) \\\Leftrightarrow & 4x+8& = &14+14+3x \\\Leftrightarrow & 4x \color{red}{+8} & = &28 \color{red}{+3x} \\\Leftrightarrow & 4x \color{red}{+8} \color{blue}{-8} \color{blue}{-3x} & = &28 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-8} \\\Leftrightarrow & 4x-3x& = &28-8 \\\Leftrightarrow & x& = &20 \\ & V = \left\{ 20 \right\} & \\\end{align}\)