Vgln. eerste graad (reeks 3)

Hoofdmenu Eentje per keer  🖨

Reeks met haakjes

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

---

Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (2x-5)& = & -11 \color{red}{+} (-11+3x) \\\Leftrightarrow & 4x-10& = &-11-11+3x \\\Leftrightarrow & 4x \color{red}{-10} & = &-22 \color{red}{+3x} \\\Leftrightarrow & 4x \color{red}{-10} \color{blue}{+10} \color{blue}{-3x} & = &-22 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+10} \\\Leftrightarrow & 4x-3x& = &-22+10 \\\Leftrightarrow & x& = &-12 \\ & V = \left\{ -12 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (-x+4)& = & 14 \color{red}{-} (-6+x) \\\Leftrightarrow & -6x+24& = &14+6-x \\\Leftrightarrow & -6x \color{red}{+24} & = &20 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{+24} \color{blue}{-24} \color{blue}{+x} & = &20 \color{red}{-x} \color{blue}{+x} \color{blue}{-24} \\\Leftrightarrow & -6x+x& = &20-24 \\\Leftrightarrow & -5x& = &-4 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-4}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{4}{5} & & \\ & V = \left\{ \frac{4}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (-2x+1)& = & 1 \color{red}{+} (-5-3x) \\\Leftrightarrow & -10x+5& = &1-5-3x \\\Leftrightarrow & -10x \color{red}{+5} & = &-4 \color{red}{-3x} \\\Leftrightarrow & -10x \color{red}{+5} \color{blue}{-5} \color{blue}{+3x} & = &-4 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-5} \\\Leftrightarrow & -10x+3x& = &-4-5 \\\Leftrightarrow & -7x& = &-9 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-9}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{9}{7} & & \\ & V = \left\{ \frac{9}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (4x-1)& = & 5 \color{red}{-} (14+x) \\\Leftrightarrow & 24x-6& = &5-14-x \\\Leftrightarrow & 24x \color{red}{-6} & = &-9 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &-9 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & 24x+x& = &-9+6 \\\Leftrightarrow & 25x& = &-3 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{-3}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{-3}{25} & & \\ & V = \left\{ \frac{-3}{25} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (5x-6)& = & -4 \color{red}{-} (10-4x) \\\Leftrightarrow & 25x-30& = &-4-10+4x \\\Leftrightarrow & 25x \color{red}{-30} & = &-14 \color{red}{+4x} \\\Leftrightarrow & 25x \color{red}{-30} \color{blue}{+30} \color{blue}{-4x} & = &-14 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+30} \\\Leftrightarrow & 25x-4x& = &-14+30 \\\Leftrightarrow & 21x& = &16 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{16}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{16}{21} & & \\ & V = \left\{ \frac{16}{21} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (6x+5)& = & -3 \color{red}{-} (-13+x) \\\Leftrightarrow & 12x+10& = &-3+13-x \\\Leftrightarrow & 12x \color{red}{+10} & = &10 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+10} \color{blue}{-10} \color{blue}{+x} & = &10 \color{red}{-x} \color{blue}{+x} \color{blue}{-10} \\\Leftrightarrow & 12x+x& = &10-10 \\\Leftrightarrow & 13x& = &0 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{0}{ \color{red}{13} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (-5x-4)& = & 7 \color{red}{-} (4+x) \\\Leftrightarrow & -30x-24& = &7-4-x \\\Leftrightarrow & -30x \color{red}{-24} & = &3 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{-24} \color{blue}{+24} \color{blue}{+x} & = &3 \color{red}{-x} \color{blue}{+x} \color{blue}{+24} \\\Leftrightarrow & -30x+x& = &3+24 \\\Leftrightarrow & -29x& = &27 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{27}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{-27}{29} & & \\ & V = \left\{ \frac{-27}{29} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (-6x-3)& = & -11 \color{red}{-} (11+x) \\\Leftrightarrow & -12x-6& = &-11-11-x \\\Leftrightarrow & -12x \color{red}{-6} & = &-22 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &-22 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & -12x+x& = &-22+6 \\\Leftrightarrow & -11x& = &-16 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-16}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{16}{11} & & \\ & V = \left\{ \frac{16}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (-5x+1)& = & 6 \color{red}{-} (-6+x) \\\Leftrightarrow & -20x+4& = &6+6-x \\\Leftrightarrow & -20x \color{red}{+4} & = &12 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{+4} \color{blue}{-4} \color{blue}{+x} & = &12 \color{red}{-x} \color{blue}{+x} \color{blue}{-4} \\\Leftrightarrow & -20x+x& = &12-4 \\\Leftrightarrow & -19x& = &8 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{8}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-8}{19} & & \\ & V = \left\{ \frac{-8}{19} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (-x-1)& = & 9 \color{red}{+} (-10-3x) \\\Leftrightarrow & -4x-4& = &9-10-3x \\\Leftrightarrow & -4x \color{red}{-4} & = &-1 \color{red}{-3x} \\\Leftrightarrow & -4x \color{red}{-4} \color{blue}{+4} \color{blue}{+3x} & = &-1 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+4} \\\Leftrightarrow & -4x+3x& = &-1+4 \\\Leftrightarrow & -x& = &3 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{3}{ \color{red}{-1} } \\\Leftrightarrow & x = -3 & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (5x+1)& = & 14 \color{red}{-} (-2+x) \\\Leftrightarrow & 20x+4& = &14+2-x \\\Leftrightarrow & 20x \color{red}{+4} & = &16 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{+4} \color{blue}{-4} \color{blue}{+x} & = &16 \color{red}{-x} \color{blue}{+x} \color{blue}{-4} \\\Leftrightarrow & 20x+x& = &16-4 \\\Leftrightarrow & 21x& = &12 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{12}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{4}{7} & & \\ & V = \left\{ \frac{4}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (2x-3)& = & 14 \color{red}{+} (12+x) \\\Leftrightarrow & 8x-12& = &14+12+x \\\Leftrightarrow & 8x \color{red}{-12} & = &26 \color{red}{+x} \\\Leftrightarrow & 8x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &26 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & 8x-x& = &26+12 \\\Leftrightarrow & 7x& = &38 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{38}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{38}{7} & & \\ & V = \left\{ \frac{38}{7} \right\} & \\\end{align}\)