Vgln. eerste graad (reeks 3)

Hoofdmenu Eentje per keer  🖨

Reeks met haakjes

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

---

Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (5x+5)& = & 9 \color{red}{-} (-6+x) \\\Leftrightarrow & 25x+25& = &9+6-x \\\Leftrightarrow & 25x \color{red}{+25} & = &15 \color{red}{-x} \\\Leftrightarrow & 25x \color{red}{+25} \color{blue}{-25} \color{blue}{+x} & = &15 \color{red}{-x} \color{blue}{+x} \color{blue}{-25} \\\Leftrightarrow & 25x+x& = &15-25 \\\Leftrightarrow & 26x& = &-10 \\\Leftrightarrow & \frac{26x}{ \color{red}{26} }& = &\frac{-10}{ \color{red}{26} } \\\Leftrightarrow & x = \frac{-5}{13} & & \\ & V = \left\{ \frac{-5}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (5x+6)& = & -6 \color{red}{-} (10+x) \\\Leftrightarrow & 25x+30& = &-6-10-x \\\Leftrightarrow & 25x \color{red}{+30} & = &-16 \color{red}{-x} \\\Leftrightarrow & 25x \color{red}{+30} \color{blue}{-30} \color{blue}{+x} & = &-16 \color{red}{-x} \color{blue}{+x} \color{blue}{-30} \\\Leftrightarrow & 25x+x& = &-16-30 \\\Leftrightarrow & 26x& = &-46 \\\Leftrightarrow & \frac{26x}{ \color{red}{26} }& = &\frac{-46}{ \color{red}{26} } \\\Leftrightarrow & x = \frac{-23}{13} & & \\ & V = \left\{ \frac{-23}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (2x+1)& = & 3 \color{red}{+} (-14+x) \\\Leftrightarrow & 12x+6& = &3-14+x \\\Leftrightarrow & 12x \color{red}{+6} & = &-11 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &-11 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & 12x-x& = &-11-6 \\\Leftrightarrow & 11x& = &-17 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-17}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-17}{11} & & \\ & V = \left\{ \frac{-17}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (2x+7)& = & -4 \color{red}{+} (-15-5x) \\\Leftrightarrow & 8x+28& = &-4-15-5x \\\Leftrightarrow & 8x \color{red}{+28} & = &-19 \color{red}{-5x} \\\Leftrightarrow & 8x \color{red}{+28} \color{blue}{-28} \color{blue}{+5x} & = &-19 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-28} \\\Leftrightarrow & 8x+5x& = &-19-28 \\\Leftrightarrow & 13x& = &-47 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-47}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-47}{13} & & \\ & V = \left\{ \frac{-47}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (6x+3)& = & -15 \color{red}{-} (-12+x) \\\Leftrightarrow & 24x+12& = &-15+12-x \\\Leftrightarrow & 24x \color{red}{+12} & = &-3 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &-3 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & 24x+x& = &-3-12 \\\Leftrightarrow & 25x& = &-15 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{-15}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{-3}{5} & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (-2x+2)& = & -4 \color{red}{+} (11+3x) \\\Leftrightarrow & -10x+10& = &-4+11+3x \\\Leftrightarrow & -10x \color{red}{+10} & = &7 \color{red}{+3x} \\\Leftrightarrow & -10x \color{red}{+10} \color{blue}{-10} \color{blue}{-3x} & = &7 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-10} \\\Leftrightarrow & -10x-3x& = &7-10 \\\Leftrightarrow & -13x& = &-3 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-3}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{3}{13} & & \\ & V = \left\{ \frac{3}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (5x+2)& = & 15 \color{red}{-} (-4+3x) \\\Leftrightarrow & 10x+4& = &15+4-3x \\\Leftrightarrow & 10x \color{red}{+4} & = &19 \color{red}{-3x} \\\Leftrightarrow & 10x \color{red}{+4} \color{blue}{-4} \color{blue}{+3x} & = &19 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-4} \\\Leftrightarrow & 10x+3x& = &19-4 \\\Leftrightarrow & 13x& = &15 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{15}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{15}{13} & & \\ & V = \left\{ \frac{15}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (-3x+1)& = & -14 \color{red}{+} (-13+x) \\\Leftrightarrow & -18x+6& = &-14-13+x \\\Leftrightarrow & -18x \color{red}{+6} & = &-27 \color{red}{+x} \\\Leftrightarrow & -18x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &-27 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & -18x-x& = &-27-6 \\\Leftrightarrow & -19x& = &-33 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-33}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{33}{19} & & \\ & V = \left\{ \frac{33}{19} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (-2x+6)& = & 13 \color{red}{-} (-4+x) \\\Leftrightarrow & -12x+36& = &13+4-x \\\Leftrightarrow & -12x \color{red}{+36} & = &17 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+36} \color{blue}{-36} \color{blue}{+x} & = &17 \color{red}{-x} \color{blue}{+x} \color{blue}{-36} \\\Leftrightarrow & -12x+x& = &17-36 \\\Leftrightarrow & -11x& = &-19 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-19}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{19}{11} & & \\ & V = \left\{ \frac{19}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (-6x-3)& = & -13 \color{red}{+} (13+x) \\\Leftrightarrow & -12x-6& = &-13+13+x \\\Leftrightarrow & -12x \color{red}{-6} & = &0 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &0 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & -12x-x& = &0+6 \\\Leftrightarrow & -13x& = &6 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{6}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-6}{13} & & \\ & V = \left\{ \frac{-6}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (x+6)& = & -7 \color{red}{-} (-6+x) \\\Leftrightarrow & 5x+30& = &-7+6-x \\\Leftrightarrow & 5x \color{red}{+30} & = &-1 \color{red}{-x} \\\Leftrightarrow & 5x \color{red}{+30} \color{blue}{-30} \color{blue}{+x} & = &-1 \color{red}{-x} \color{blue}{+x} \color{blue}{-30} \\\Leftrightarrow & 5x+x& = &-1-30 \\\Leftrightarrow & 6x& = &-31 \\\Leftrightarrow & \frac{6x}{ \color{red}{6} }& = &\frac{-31}{ \color{red}{6} } \\\Leftrightarrow & x = \frac{-31}{6} & & \\ & V = \left\{ \frac{-31}{6} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (-2x+1)& = & 5 \color{red}{-} (5+x) \\\Leftrightarrow & -12x+6& = &5-5-x \\\Leftrightarrow & -12x \color{red}{+6} & = &0 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+6} \color{blue}{-6} \color{blue}{+x} & = &0 \color{red}{-x} \color{blue}{+x} \color{blue}{-6} \\\Leftrightarrow & -12x+x& = &0-6 \\\Leftrightarrow & -11x& = &-6 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-6}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{6}{11} & & \\ & V = \left\{ \frac{6}{11} \right\} & \\\end{align}\)