Vgln. eerste graad (reeks 3)

Hoofdmenu Eentje per keer  🖨

Reeks met haakjes

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

---

Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (-3x+4)& = & -9 \color{red}{+} (-10-5x) \\\Leftrightarrow & -18x+24& = &-9-10-5x \\\Leftrightarrow & -18x \color{red}{+24} & = &-19 \color{red}{-5x} \\\Leftrightarrow & -18x \color{red}{+24} \color{blue}{-24} \color{blue}{+5x} & = &-19 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-24} \\\Leftrightarrow & -18x+5x& = &-19-24 \\\Leftrightarrow & -13x& = &-43 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-43}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{43}{13} & & \\ & V = \left\{ \frac{43}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (3x-2)& = & -4 \color{red}{-} (2+x) \\\Leftrightarrow & 12x-8& = &-4-2-x \\\Leftrightarrow & 12x \color{red}{-8} & = &-6 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-8} \color{blue}{+8} \color{blue}{+x} & = &-6 \color{red}{-x} \color{blue}{+x} \color{blue}{+8} \\\Leftrightarrow & 12x+x& = &-6+8 \\\Leftrightarrow & 13x& = &2 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{2}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{2}{13} & & \\ & V = \left\{ \frac{2}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (5x+2)& = & -5 \color{red}{-} (-13+x) \\\Leftrightarrow & 20x+8& = &-5+13-x \\\Leftrightarrow & 20x \color{red}{+8} & = &8 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{+8} \color{blue}{-8} \color{blue}{+x} & = &8 \color{red}{-x} \color{blue}{+x} \color{blue}{-8} \\\Leftrightarrow & 20x+x& = &8-8 \\\Leftrightarrow & 21x& = &0 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{0}{ \color{red}{21} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (3x-6)& = & -1 \color{red}{+} (-7+4x) \\\Leftrightarrow & 9x-18& = &-1-7+4x \\\Leftrightarrow & 9x \color{red}{-18} & = &-8 \color{red}{+4x} \\\Leftrightarrow & 9x \color{red}{-18} \color{blue}{+18} \color{blue}{-4x} & = &-8 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+18} \\\Leftrightarrow & 9x-4x& = &-8+18 \\\Leftrightarrow & 5x& = &10 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{10}{ \color{red}{5} } \\\Leftrightarrow & x = 2 & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (5x+2)& = & 7 \color{red}{-} (2+x) \\\Leftrightarrow & 15x+6& = &7-2-x \\\Leftrightarrow & 15x \color{red}{+6} & = &5 \color{red}{-x} \\\Leftrightarrow & 15x \color{red}{+6} \color{blue}{-6} \color{blue}{+x} & = &5 \color{red}{-x} \color{blue}{+x} \color{blue}{-6} \\\Leftrightarrow & 15x+x& = &5-6 \\\Leftrightarrow & 16x& = &-1 \\\Leftrightarrow & \frac{16x}{ \color{red}{16} }& = &\frac{-1}{ \color{red}{16} } \\\Leftrightarrow & x = \frac{-1}{16} & & \\ & V = \left\{ \frac{-1}{16} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (-x+1)& = & -15 \color{red}{+} (9+4x) \\\Leftrightarrow & -5x+5& = &-15+9+4x \\\Leftrightarrow & -5x \color{red}{+5} & = &-6 \color{red}{+4x} \\\Leftrightarrow & -5x \color{red}{+5} \color{blue}{-5} \color{blue}{-4x} & = &-6 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-5} \\\Leftrightarrow & -5x-4x& = &-6-5 \\\Leftrightarrow & -9x& = &-11 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{-11}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{11}{9} & & \\ & V = \left\{ \frac{11}{9} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (-5x-2)& = & 6 \color{red}{+} (11+x) \\\Leftrightarrow & -25x-10& = &6+11+x \\\Leftrightarrow & -25x \color{red}{-10} & = &17 \color{red}{+x} \\\Leftrightarrow & -25x \color{red}{-10} \color{blue}{+10} \color{blue}{-x} & = &17 \color{red}{+x} \color{blue}{-x} \color{blue}{+10} \\\Leftrightarrow & -25x-x& = &17+10 \\\Leftrightarrow & -26x& = &27 \\\Leftrightarrow & \frac{-26x}{ \color{red}{-26} }& = &\frac{27}{ \color{red}{-26} } \\\Leftrightarrow & x = \frac{-27}{26} & & \\ & V = \left\{ \frac{-27}{26} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (6x-5)& = & 15 \color{red}{+} (1-5x) \\\Leftrightarrow & 18x-15& = &15+1-5x \\\Leftrightarrow & 18x \color{red}{-15} & = &16 \color{red}{-5x} \\\Leftrightarrow & 18x \color{red}{-15} \color{blue}{+15} \color{blue}{+5x} & = &16 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+15} \\\Leftrightarrow & 18x+5x& = &16+15 \\\Leftrightarrow & 23x& = &31 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{31}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{31}{23} & & \\ & V = \left\{ \frac{31}{23} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (-4x-2)& = & 11 \color{red}{-} (-5+x) \\\Leftrightarrow & -16x-8& = &11+5-x \\\Leftrightarrow & -16x \color{red}{-8} & = &16 \color{red}{-x} \\\Leftrightarrow & -16x \color{red}{-8} \color{blue}{+8} \color{blue}{+x} & = &16 \color{red}{-x} \color{blue}{+x} \color{blue}{+8} \\\Leftrightarrow & -16x+x& = &16+8 \\\Leftrightarrow & -15x& = &24 \\\Leftrightarrow & \frac{-15x}{ \color{red}{-15} }& = &\frac{24}{ \color{red}{-15} } \\\Leftrightarrow & x = \frac{-8}{5} & & \\ & V = \left\{ \frac{-8}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (6x-4)& = & 7 \color{red}{-} (3+x) \\\Leftrightarrow & 18x-12& = &7-3-x \\\Leftrightarrow & 18x \color{red}{-12} & = &4 \color{red}{-x} \\\Leftrightarrow & 18x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &4 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & 18x+x& = &4+12 \\\Leftrightarrow & 19x& = &16 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{16}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{16}{19} & & \\ & V = \left\{ \frac{16}{19} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (2x+5)& = & 14 \color{red}{-} (2+x) \\\Leftrightarrow & 12x+30& = &14-2-x \\\Leftrightarrow & 12x \color{red}{+30} & = &12 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+30} \color{blue}{-30} \color{blue}{+x} & = &12 \color{red}{-x} \color{blue}{+x} \color{blue}{-30} \\\Leftrightarrow & 12x+x& = &12-30 \\\Leftrightarrow & 13x& = &-18 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-18}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-18}{13} & & \\ & V = \left\{ \frac{-18}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (3x+5)& = & -13 \color{red}{+} (-4+4x) \\\Leftrightarrow & 15x+25& = &-13-4+4x \\\Leftrightarrow & 15x \color{red}{+25} & = &-17 \color{red}{+4x} \\\Leftrightarrow & 15x \color{red}{+25} \color{blue}{-25} \color{blue}{-4x} & = &-17 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-25} \\\Leftrightarrow & 15x-4x& = &-17-25 \\\Leftrightarrow & 11x& = &-42 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-42}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-42}{11} & & \\ & V = \left\{ \frac{-42}{11} \right\} & \\\end{align}\)