Vgln. eerste graad (reeks 3)

Hoofdmenu Eentje per keer  🖨

Reeks met haakjes

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

---

Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (-4x+5)& = & 14 \color{red}{-} (1+x) \\\Leftrightarrow & -20x+25& = &14-1-x \\\Leftrightarrow & -20x \color{red}{+25} & = &13 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{+25} \color{blue}{-25} \color{blue}{+x} & = &13 \color{red}{-x} \color{blue}{+x} \color{blue}{-25} \\\Leftrightarrow & -20x+x& = &13-25 \\\Leftrightarrow & -19x& = &-12 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-12}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{12}{19} & & \\ & V = \left\{ \frac{12}{19} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (-6x+5)& = & 6 \color{red}{-} (-14+x) \\\Leftrightarrow & -12x+10& = &6+14-x \\\Leftrightarrow & -12x \color{red}{+10} & = &20 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+10} \color{blue}{-10} \color{blue}{+x} & = &20 \color{red}{-x} \color{blue}{+x} \color{blue}{-10} \\\Leftrightarrow & -12x+x& = &20-10 \\\Leftrightarrow & -11x& = &10 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{10}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-10}{11} & & \\ & V = \left\{ \frac{-10}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (2x-5)& = & 12 \color{red}{-} (9+x) \\\Leftrightarrow & 8x-20& = &12-9-x \\\Leftrightarrow & 8x \color{red}{-20} & = &3 \color{red}{-x} \\\Leftrightarrow & 8x \color{red}{-20} \color{blue}{+20} \color{blue}{+x} & = &3 \color{red}{-x} \color{blue}{+x} \color{blue}{+20} \\\Leftrightarrow & 8x+x& = &3+20 \\\Leftrightarrow & 9x& = &23 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{23}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{23}{9} & & \\ & V = \left\{ \frac{23}{9} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (5x+1)& = & -9 \color{red}{-} (-14-4x) \\\Leftrightarrow & 25x+5& = &-9+14+4x \\\Leftrightarrow & 25x \color{red}{+5} & = &5 \color{red}{+4x} \\\Leftrightarrow & 25x \color{red}{+5} \color{blue}{-5} \color{blue}{-4x} & = &5 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-5} \\\Leftrightarrow & 25x-4x& = &5-5 \\\Leftrightarrow & 21x& = &0 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{0}{ \color{red}{21} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (2x+7)& = & -4 \color{red}{+} (-14+x) \\\Leftrightarrow & 6x+21& = &-4-14+x \\\Leftrightarrow & 6x \color{red}{+21} & = &-18 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{+21} \color{blue}{-21} \color{blue}{-x} & = &-18 \color{red}{+x} \color{blue}{-x} \color{blue}{-21} \\\Leftrightarrow & 6x-x& = &-18-21 \\\Leftrightarrow & 5x& = &-39 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-39}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{-39}{5} & & \\ & V = \left\{ \frac{-39}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (5x-5)& = & 12 \color{red}{-} (-15+x) \\\Leftrightarrow & 20x-20& = &12+15-x \\\Leftrightarrow & 20x \color{red}{-20} & = &27 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{-20} \color{blue}{+20} \color{blue}{+x} & = &27 \color{red}{-x} \color{blue}{+x} \color{blue}{+20} \\\Leftrightarrow & 20x+x& = &27+20 \\\Leftrightarrow & 21x& = &47 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{47}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{47}{21} & & \\ & V = \left\{ \frac{47}{21} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (5x-6)& = & 15 \color{red}{-} (12+x) \\\Leftrightarrow & 30x-36& = &15-12-x \\\Leftrightarrow & 30x \color{red}{-36} & = &3 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{-36} \color{blue}{+36} \color{blue}{+x} & = &3 \color{red}{-x} \color{blue}{+x} \color{blue}{+36} \\\Leftrightarrow & 30x+x& = &3+36 \\\Leftrightarrow & 31x& = &39 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{39}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{39}{31} & & \\ & V = \left\{ \frac{39}{31} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (-5x+1)& = & -8 \color{red}{-} (-15+x) \\\Leftrightarrow & -20x+4& = &-8+15-x \\\Leftrightarrow & -20x \color{red}{+4} & = &7 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{+4} \color{blue}{-4} \color{blue}{+x} & = &7 \color{red}{-x} \color{blue}{+x} \color{blue}{-4} \\\Leftrightarrow & -20x+x& = &7-4 \\\Leftrightarrow & -19x& = &3 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{3}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-3}{19} & & \\ & V = \left\{ \frac{-3}{19} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (3x-5)& = & 14 \color{red}{+} (6-2x) \\\Leftrightarrow & 15x-25& = &14+6-2x \\\Leftrightarrow & 15x \color{red}{-25} & = &20 \color{red}{-2x} \\\Leftrightarrow & 15x \color{red}{-25} \color{blue}{+25} \color{blue}{+2x} & = &20 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+25} \\\Leftrightarrow & 15x+2x& = &20+25 \\\Leftrightarrow & 17x& = &45 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{45}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{45}{17} & & \\ & V = \left\{ \frac{45}{17} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (-4x+6)& = & 7 \color{red}{-} (-12-3x) \\\Leftrightarrow & -16x+24& = &7+12+3x \\\Leftrightarrow & -16x \color{red}{+24} & = &19 \color{red}{+3x} \\\Leftrightarrow & -16x \color{red}{+24} \color{blue}{-24} \color{blue}{-3x} & = &19 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-24} \\\Leftrightarrow & -16x-3x& = &19-24 \\\Leftrightarrow & -19x& = &-5 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-5}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{5}{19} & & \\ & V = \left\{ \frac{5}{19} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (x+5)& = & 9 \color{red}{-} (-2+x) \\\Leftrightarrow & 4x+20& = &9+2-x \\\Leftrightarrow & 4x \color{red}{+20} & = &11 \color{red}{-x} \\\Leftrightarrow & 4x \color{red}{+20} \color{blue}{-20} \color{blue}{+x} & = &11 \color{red}{-x} \color{blue}{+x} \color{blue}{-20} \\\Leftrightarrow & 4x+x& = &11-20 \\\Leftrightarrow & 5x& = &-9 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-9}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{-9}{5} & & \\ & V = \left\{ \frac{-9}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (-2x-3)& = & -4 \color{red}{+} (12+x) \\\Leftrightarrow & -10x-15& = &-4+12+x \\\Leftrightarrow & -10x \color{red}{-15} & = &8 \color{red}{+x} \\\Leftrightarrow & -10x \color{red}{-15} \color{blue}{+15} \color{blue}{-x} & = &8 \color{red}{+x} \color{blue}{-x} \color{blue}{+15} \\\Leftrightarrow & -10x-x& = &8+15 \\\Leftrightarrow & -11x& = &23 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{23}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-23}{11} & & \\ & V = \left\{ \frac{-23}{11} \right\} & \\\end{align}\)