Vgln. eerste graad (reeks 3)

Hoofdmenu Eentje per keer  🖨

Reeks met haakjes

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

---

Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (-3x-3)& = & 2 \color{red}{-} (-3-5x) \\\Leftrightarrow & -18x-18& = &2+3+5x \\\Leftrightarrow & -18x \color{red}{-18} & = &5 \color{red}{+5x} \\\Leftrightarrow & -18x \color{red}{-18} \color{blue}{+18} \color{blue}{-5x} & = &5 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+18} \\\Leftrightarrow & -18x-5x& = &5+18 \\\Leftrightarrow & -23x& = &23 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{23}{ \color{red}{-23} } \\\Leftrightarrow & x = -1 & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (-3x-6)& = & -13 \color{red}{-} (14-4x) \\\Leftrightarrow & -9x-18& = &-13-14+4x \\\Leftrightarrow & -9x \color{red}{-18} & = &-27 \color{red}{+4x} \\\Leftrightarrow & -9x \color{red}{-18} \color{blue}{+18} \color{blue}{-4x} & = &-27 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+18} \\\Leftrightarrow & -9x-4x& = &-27+18 \\\Leftrightarrow & -13x& = &-9 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-9}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{9}{13} & & \\ & V = \left\{ \frac{9}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (4x+5)& = & 14 \color{red}{-} (-5-5x) \\\Leftrightarrow & 16x+20& = &14+5+5x \\\Leftrightarrow & 16x \color{red}{+20} & = &19 \color{red}{+5x} \\\Leftrightarrow & 16x \color{red}{+20} \color{blue}{-20} \color{blue}{-5x} & = &19 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-20} \\\Leftrightarrow & 16x-5x& = &19-20 \\\Leftrightarrow & 11x& = &-1 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-1}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-1}{11} & & \\ & V = \left\{ \frac{-1}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (-4x-7)& = & 13 \color{red}{-} (9+x) \\\Leftrightarrow & -8x-14& = &13-9-x \\\Leftrightarrow & -8x \color{red}{-14} & = &4 \color{red}{-x} \\\Leftrightarrow & -8x \color{red}{-14} \color{blue}{+14} \color{blue}{+x} & = &4 \color{red}{-x} \color{blue}{+x} \color{blue}{+14} \\\Leftrightarrow & -8x+x& = &4+14 \\\Leftrightarrow & -7x& = &18 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{18}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-18}{7} & & \\ & V = \left\{ \frac{-18}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (-4x-7)& = & 6 \color{red}{+} (-11+x) \\\Leftrightarrow & -20x-35& = &6-11+x \\\Leftrightarrow & -20x \color{red}{-35} & = &-5 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{-35} \color{blue}{+35} \color{blue}{-x} & = &-5 \color{red}{+x} \color{blue}{-x} \color{blue}{+35} \\\Leftrightarrow & -20x-x& = &-5+35 \\\Leftrightarrow & -21x& = &30 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{30}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{-10}{7} & & \\ & V = \left\{ \frac{-10}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (2x+7)& = & -1 \color{red}{+} (-14-5x) \\\Leftrightarrow & 6x+21& = &-1-14-5x \\\Leftrightarrow & 6x \color{red}{+21} & = &-15 \color{red}{-5x} \\\Leftrightarrow & 6x \color{red}{+21} \color{blue}{-21} \color{blue}{+5x} & = &-15 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-21} \\\Leftrightarrow & 6x+5x& = &-15-21 \\\Leftrightarrow & 11x& = &-36 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-36}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-36}{11} & & \\ & V = \left\{ \frac{-36}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (-x-3)& = & -1 \color{red}{-} (-3-5x) \\\Leftrightarrow & -3x-9& = &-1+3+5x \\\Leftrightarrow & -3x \color{red}{-9} & = &2 \color{red}{+5x} \\\Leftrightarrow & -3x \color{red}{-9} \color{blue}{+9} \color{blue}{-5x} & = &2 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+9} \\\Leftrightarrow & -3x-5x& = &2+9 \\\Leftrightarrow & -8x& = &11 \\\Leftrightarrow & \frac{-8x}{ \color{red}{-8} }& = &\frac{11}{ \color{red}{-8} } \\\Leftrightarrow & x = \frac{-11}{8} & & \\ & V = \left\{ \frac{-11}{8} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (5x-5)& = & 3 \color{red}{+} (10-3x) \\\Leftrightarrow & 25x-25& = &3+10-3x \\\Leftrightarrow & 25x \color{red}{-25} & = &13 \color{red}{-3x} \\\Leftrightarrow & 25x \color{red}{-25} \color{blue}{+25} \color{blue}{+3x} & = &13 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+25} \\\Leftrightarrow & 25x+3x& = &13+25 \\\Leftrightarrow & 28x& = &38 \\\Leftrightarrow & \frac{28x}{ \color{red}{28} }& = &\frac{38}{ \color{red}{28} } \\\Leftrightarrow & x = \frac{19}{14} & & \\ & V = \left\{ \frac{19}{14} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (-x+1)& = & -1 \color{red}{-} (8-3x) \\\Leftrightarrow & -4x+4& = &-1-8+3x \\\Leftrightarrow & -4x \color{red}{+4} & = &-9 \color{red}{+3x} \\\Leftrightarrow & -4x \color{red}{+4} \color{blue}{-4} \color{blue}{-3x} & = &-9 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-4} \\\Leftrightarrow & -4x-3x& = &-9-4 \\\Leftrightarrow & -7x& = &-13 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-13}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{13}{7} & & \\ & V = \left\{ \frac{13}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (5x+4)& = & 15 \color{red}{+} (10+4x) \\\Leftrightarrow & 15x+12& = &15+10+4x \\\Leftrightarrow & 15x \color{red}{+12} & = &25 \color{red}{+4x} \\\Leftrightarrow & 15x \color{red}{+12} \color{blue}{-12} \color{blue}{-4x} & = &25 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-12} \\\Leftrightarrow & 15x-4x& = &25-12 \\\Leftrightarrow & 11x& = &13 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{13}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{13}{11} & & \\ & V = \left\{ \frac{13}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (-5x-2)& = & -12 \color{red}{-} (-11+x) \\\Leftrightarrow & -20x-8& = &-12+11-x \\\Leftrightarrow & -20x \color{red}{-8} & = &-1 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{-8} \color{blue}{+8} \color{blue}{+x} & = &-1 \color{red}{-x} \color{blue}{+x} \color{blue}{+8} \\\Leftrightarrow & -20x+x& = &-1+8 \\\Leftrightarrow & -19x& = &7 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{7}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-7}{19} & & \\ & V = \left\{ \frac{-7}{19} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (5x+2)& = & 10 \color{red}{-} (-2+x) \\\Leftrightarrow & 30x+12& = &10+2-x \\\Leftrightarrow & 30x \color{red}{+12} & = &12 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &12 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & 30x+x& = &12-12 \\\Leftrightarrow & 31x& = &0 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{0}{ \color{red}{31} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)