Vgln. eerste graad (reeks 3)

Hoofdmenu Eentje per keer  🖨

Reeks met haakjes

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

---

Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (-6x+7)& = & 6 \color{red}{+} (5-5x) \\\Leftrightarrow & -36x+42& = &6+5-5x \\\Leftrightarrow & -36x \color{red}{+42} & = &11 \color{red}{-5x} \\\Leftrightarrow & -36x \color{red}{+42} \color{blue}{-42} \color{blue}{+5x} & = &11 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-42} \\\Leftrightarrow & -36x+5x& = &11-42 \\\Leftrightarrow & -31x& = &-31 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{-31}{ \color{red}{-31} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (-4x-1)& = & -2 \color{red}{-} (-4+x) \\\Leftrightarrow & -20x-5& = &-2+4-x \\\Leftrightarrow & -20x \color{red}{-5} & = &2 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{-5} \color{blue}{+5} \color{blue}{+x} & = &2 \color{red}{-x} \color{blue}{+x} \color{blue}{+5} \\\Leftrightarrow & -20x+x& = &2+5 \\\Leftrightarrow & -19x& = &7 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{7}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-7}{19} & & \\ & V = \left\{ \frac{-7}{19} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (6x+5)& = & -14 \color{red}{-} (13+x) \\\Leftrightarrow & 18x+15& = &-14-13-x \\\Leftrightarrow & 18x \color{red}{+15} & = &-27 \color{red}{-x} \\\Leftrightarrow & 18x \color{red}{+15} \color{blue}{-15} \color{blue}{+x} & = &-27 \color{red}{-x} \color{blue}{+x} \color{blue}{-15} \\\Leftrightarrow & 18x+x& = &-27-15 \\\Leftrightarrow & 19x& = &-42 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-42}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-42}{19} & & \\ & V = \left\{ \frac{-42}{19} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (-4x+3)& = & 4 \color{red}{-} (6+x) \\\Leftrightarrow & -20x+15& = &4-6-x \\\Leftrightarrow & -20x \color{red}{+15} & = &-2 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{+15} \color{blue}{-15} \color{blue}{+x} & = &-2 \color{red}{-x} \color{blue}{+x} \color{blue}{-15} \\\Leftrightarrow & -20x+x& = &-2-15 \\\Leftrightarrow & -19x& = &-17 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-17}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{17}{19} & & \\ & V = \left\{ \frac{17}{19} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (-4x+5)& = & -6 \color{red}{-} (-12+x) \\\Leftrightarrow & -8x+10& = &-6+12-x \\\Leftrightarrow & -8x \color{red}{+10} & = &6 \color{red}{-x} \\\Leftrightarrow & -8x \color{red}{+10} \color{blue}{-10} \color{blue}{+x} & = &6 \color{red}{-x} \color{blue}{+x} \color{blue}{-10} \\\Leftrightarrow & -8x+x& = &6-10 \\\Leftrightarrow & -7x& = &-4 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-4}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{4}{7} & & \\ & V = \left\{ \frac{4}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (3x+4)& = & 7 \color{red}{+} (-9-2x) \\\Leftrightarrow & 15x+20& = &7-9-2x \\\Leftrightarrow & 15x \color{red}{+20} & = &-2 \color{red}{-2x} \\\Leftrightarrow & 15x \color{red}{+20} \color{blue}{-20} \color{blue}{+2x} & = &-2 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-20} \\\Leftrightarrow & 15x+2x& = &-2-20 \\\Leftrightarrow & 17x& = &-22 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{-22}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{-22}{17} & & \\ & V = \left\{ \frac{-22}{17} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (5x-5)& = & -6 \color{red}{-} (7+x) \\\Leftrightarrow & 30x-30& = &-6-7-x \\\Leftrightarrow & 30x \color{red}{-30} & = &-13 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{-30} \color{blue}{+30} \color{blue}{+x} & = &-13 \color{red}{-x} \color{blue}{+x} \color{blue}{+30} \\\Leftrightarrow & 30x+x& = &-13+30 \\\Leftrightarrow & 31x& = &17 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{17}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{17}{31} & & \\ & V = \left\{ \frac{17}{31} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (-6x-3)& = & -8 \color{red}{-} (12-5x) \\\Leftrightarrow & -36x-18& = &-8-12+5x \\\Leftrightarrow & -36x \color{red}{-18} & = &-20 \color{red}{+5x} \\\Leftrightarrow & -36x \color{red}{-18} \color{blue}{+18} \color{blue}{-5x} & = &-20 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+18} \\\Leftrightarrow & -36x-5x& = &-20+18 \\\Leftrightarrow & -41x& = &-2 \\\Leftrightarrow & \frac{-41x}{ \color{red}{-41} }& = &\frac{-2}{ \color{red}{-41} } \\\Leftrightarrow & x = \frac{2}{41} & & \\ & V = \left\{ \frac{2}{41} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (-6x-6)& = & 2 \color{red}{+} (5-5x) \\\Leftrightarrow & -18x-18& = &2+5-5x \\\Leftrightarrow & -18x \color{red}{-18} & = &7 \color{red}{-5x} \\\Leftrightarrow & -18x \color{red}{-18} \color{blue}{+18} \color{blue}{+5x} & = &7 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+18} \\\Leftrightarrow & -18x+5x& = &7+18 \\\Leftrightarrow & -13x& = &25 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{25}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-25}{13} & & \\ & V = \left\{ \frac{-25}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (6x-4)& = & -1 \color{red}{+} (-5+x) \\\Leftrightarrow & 24x-16& = &-1-5+x \\\Leftrightarrow & 24x \color{red}{-16} & = &-6 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{-16} \color{blue}{+16} \color{blue}{-x} & = &-6 \color{red}{+x} \color{blue}{-x} \color{blue}{+16} \\\Leftrightarrow & 24x-x& = &-6+16 \\\Leftrightarrow & 23x& = &10 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{10}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{10}{23} & & \\ & V = \left\{ \frac{10}{23} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (-3x+3)& = & -13 \color{red}{-} (-5+x) \\\Leftrightarrow & -12x+12& = &-13+5-x \\\Leftrightarrow & -12x \color{red}{+12} & = &-8 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &-8 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & -12x+x& = &-8-12 \\\Leftrightarrow & -11x& = &-20 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-20}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{20}{11} & & \\ & V = \left\{ \frac{20}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (3x-4)& = & 11 \color{red}{+} (-7+x) \\\Leftrightarrow & 12x-16& = &11-7+x \\\Leftrightarrow & 12x \color{red}{-16} & = &4 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-16} \color{blue}{+16} \color{blue}{-x} & = &4 \color{red}{+x} \color{blue}{-x} \color{blue}{+16} \\\Leftrightarrow & 12x-x& = &4+16 \\\Leftrightarrow & 11x& = &20 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{20}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{20}{11} & & \\ & V = \left\{ \frac{20}{11} \right\} & \\\end{align}\)