Vgln. eerste graad (reeks 3)

Hoofdmenu Eentje per keer  🖨

Reeks met haakjes

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

---

Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (3x-4)& = & -11 \color{red}{-} (-2+x) \\\Leftrightarrow & 12x-16& = &-11+2-x \\\Leftrightarrow & 12x \color{red}{-16} & = &-9 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-16} \color{blue}{+16} \color{blue}{+x} & = &-9 \color{red}{-x} \color{blue}{+x} \color{blue}{+16} \\\Leftrightarrow & 12x+x& = &-9+16 \\\Leftrightarrow & 13x& = &7 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{7}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{7}{13} & & \\ & V = \left\{ \frac{7}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (6x-5)& = & 6 \color{red}{-} (8+x) \\\Leftrightarrow & 18x-15& = &6-8-x \\\Leftrightarrow & 18x \color{red}{-15} & = &-2 \color{red}{-x} \\\Leftrightarrow & 18x \color{red}{-15} \color{blue}{+15} \color{blue}{+x} & = &-2 \color{red}{-x} \color{blue}{+x} \color{blue}{+15} \\\Leftrightarrow & 18x+x& = &-2+15 \\\Leftrightarrow & 19x& = &13 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{13}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{13}{19} & & \\ & V = \left\{ \frac{13}{19} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (4x+5)& = & -2 \color{red}{-} (-13+x) \\\Leftrightarrow & 12x+15& = &-2+13-x \\\Leftrightarrow & 12x \color{red}{+15} & = &11 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+15} \color{blue}{-15} \color{blue}{+x} & = &11 \color{red}{-x} \color{blue}{+x} \color{blue}{-15} \\\Leftrightarrow & 12x+x& = &11-15 \\\Leftrightarrow & 13x& = &-4 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-4}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-4}{13} & & \\ & V = \left\{ \frac{-4}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (-4x-3)& = & 8 \color{red}{-} (-9+x) \\\Leftrightarrow & -20x-15& = &8+9-x \\\Leftrightarrow & -20x \color{red}{-15} & = &17 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{-15} \color{blue}{+15} \color{blue}{+x} & = &17 \color{red}{-x} \color{blue}{+x} \color{blue}{+15} \\\Leftrightarrow & -20x+x& = &17+15 \\\Leftrightarrow & -19x& = &32 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{32}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-32}{19} & & \\ & V = \left\{ \frac{-32}{19} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (5x+2)& = & 11 \color{red}{-} (-2+x) \\\Leftrightarrow & 25x+10& = &11+2-x \\\Leftrightarrow & 25x \color{red}{+10} & = &13 \color{red}{-x} \\\Leftrightarrow & 25x \color{red}{+10} \color{blue}{-10} \color{blue}{+x} & = &13 \color{red}{-x} \color{blue}{+x} \color{blue}{-10} \\\Leftrightarrow & 25x+x& = &13-10 \\\Leftrightarrow & 26x& = &3 \\\Leftrightarrow & \frac{26x}{ \color{red}{26} }& = &\frac{3}{ \color{red}{26} } \\\Leftrightarrow & x = \frac{3}{26} & & \\ & V = \left\{ \frac{3}{26} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (4x-5)& = & -9 \color{red}{+} (-3+x) \\\Leftrightarrow & 12x-15& = &-9-3+x \\\Leftrightarrow & 12x \color{red}{-15} & = &-12 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-15} \color{blue}{+15} \color{blue}{-x} & = &-12 \color{red}{+x} \color{blue}{-x} \color{blue}{+15} \\\Leftrightarrow & 12x-x& = &-12+15 \\\Leftrightarrow & 11x& = &3 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{3}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{3}{11} & & \\ & V = \left\{ \frac{3}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (-6x+1)& = & 7 \color{red}{-} (4+x) \\\Leftrightarrow & -30x+5& = &7-4-x \\\Leftrightarrow & -30x \color{red}{+5} & = &3 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{+5} \color{blue}{-5} \color{blue}{+x} & = &3 \color{red}{-x} \color{blue}{+x} \color{blue}{-5} \\\Leftrightarrow & -30x+x& = &3-5 \\\Leftrightarrow & -29x& = &-2 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{-2}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{2}{29} & & \\ & V = \left\{ \frac{2}{29} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (-4x+1)& = & -5 \color{red}{+} (3-5x) \\\Leftrightarrow & -8x+2& = &-5+3-5x \\\Leftrightarrow & -8x \color{red}{+2} & = &-2 \color{red}{-5x} \\\Leftrightarrow & -8x \color{red}{+2} \color{blue}{-2} \color{blue}{+5x} & = &-2 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-2} \\\Leftrightarrow & -8x+5x& = &-2-2 \\\Leftrightarrow & -3x& = &-4 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{-4}{ \color{red}{-3} } \\\Leftrightarrow & x = \frac{4}{3} & & \\ & V = \left\{ \frac{4}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (5x+7)& = & 6 \color{red}{+} (-7+x) \\\Leftrightarrow & 30x+42& = &6-7+x \\\Leftrightarrow & 30x \color{red}{+42} & = &-1 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{+42} \color{blue}{-42} \color{blue}{-x} & = &-1 \color{red}{+x} \color{blue}{-x} \color{blue}{-42} \\\Leftrightarrow & 30x-x& = &-1-42 \\\Leftrightarrow & 29x& = &-43 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{-43}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{-43}{29} & & \\ & V = \left\{ \frac{-43}{29} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (2x+6)& = & 2 \color{red}{-} (-3+x) \\\Leftrightarrow & 4x+12& = &2+3-x \\\Leftrightarrow & 4x \color{red}{+12} & = &5 \color{red}{-x} \\\Leftrightarrow & 4x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &5 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & 4x+x& = &5-12 \\\Leftrightarrow & 5x& = &-7 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-7}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{-7}{5} & & \\ & V = \left\{ \frac{-7}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (-x-3)& = & 4 \color{red}{+} (-4+2x) \\\Leftrightarrow & -3x-9& = &4-4+2x \\\Leftrightarrow & -3x \color{red}{-9} & = &0 \color{red}{+2x} \\\Leftrightarrow & -3x \color{red}{-9} \color{blue}{+9} \color{blue}{-2x} & = &0 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+9} \\\Leftrightarrow & -3x-2x& = &0+9 \\\Leftrightarrow & -5x& = &9 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{9}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-9}{5} & & \\ & V = \left\{ \frac{-9}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (-6x-4)& = & -11 \color{red}{+} (7+x) \\\Leftrightarrow & -36x-24& = &-11+7+x \\\Leftrightarrow & -36x \color{red}{-24} & = &-4 \color{red}{+x} \\\Leftrightarrow & -36x \color{red}{-24} \color{blue}{+24} \color{blue}{-x} & = &-4 \color{red}{+x} \color{blue}{-x} \color{blue}{+24} \\\Leftrightarrow & -36x-x& = &-4+24 \\\Leftrightarrow & -37x& = &20 \\\Leftrightarrow & \frac{-37x}{ \color{red}{-37} }& = &\frac{20}{ \color{red}{-37} } \\\Leftrightarrow & x = \frac{-20}{37} & & \\ & V = \left\{ \frac{-20}{37} \right\} & \\\end{align}\)