Vgln. eerste graad (reeks 3)

Hoofdmenu Eentje per keer  🖨

Reeks met haakjes

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

---

Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (x-4)& = & 5 \color{red}{+} (-2+2x) \\\Leftrightarrow & 3x-12& = &5-2+2x \\\Leftrightarrow & 3x \color{red}{-12} & = &3 \color{red}{+2x} \\\Leftrightarrow & 3x \color{red}{-12} \color{blue}{+12} \color{blue}{-2x} & = &3 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+12} \\\Leftrightarrow & 3x-2x& = &3+12 \\\Leftrightarrow & x& = &15 \\ & V = \left\{ 15 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (4x-3)& = & -11 \color{red}{-} (14+x) \\\Leftrightarrow & 24x-18& = &-11-14-x \\\Leftrightarrow & 24x \color{red}{-18} & = &-25 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{-18} \color{blue}{+18} \color{blue}{+x} & = &-25 \color{red}{-x} \color{blue}{+x} \color{blue}{+18} \\\Leftrightarrow & 24x+x& = &-25+18 \\\Leftrightarrow & 25x& = &-7 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{-7}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{-7}{25} & & \\ & V = \left\{ \frac{-7}{25} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (-2x-7)& = & 4 \color{red}{-} (-9+x) \\\Leftrightarrow & -6x-21& = &4+9-x \\\Leftrightarrow & -6x \color{red}{-21} & = &13 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{-21} \color{blue}{+21} \color{blue}{+x} & = &13 \color{red}{-x} \color{blue}{+x} \color{blue}{+21} \\\Leftrightarrow & -6x+x& = &13+21 \\\Leftrightarrow & -5x& = &34 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{34}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-34}{5} & & \\ & V = \left\{ \frac{-34}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (5x+4)& = & 12 \color{red}{+} (-8+x) \\\Leftrightarrow & 30x+24& = &12-8+x \\\Leftrightarrow & 30x \color{red}{+24} & = &4 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{+24} \color{blue}{-24} \color{blue}{-x} & = &4 \color{red}{+x} \color{blue}{-x} \color{blue}{-24} \\\Leftrightarrow & 30x-x& = &4-24 \\\Leftrightarrow & 29x& = &-20 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{-20}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{-20}{29} & & \\ & V = \left\{ \frac{-20}{29} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (-2x-7)& = & 7 \color{red}{-} (9+x) \\\Leftrightarrow & -10x-35& = &7-9-x \\\Leftrightarrow & -10x \color{red}{-35} & = &-2 \color{red}{-x} \\\Leftrightarrow & -10x \color{red}{-35} \color{blue}{+35} \color{blue}{+x} & = &-2 \color{red}{-x} \color{blue}{+x} \color{blue}{+35} \\\Leftrightarrow & -10x+x& = &-2+35 \\\Leftrightarrow & -9x& = &33 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{33}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{-11}{3} & & \\ & V = \left\{ \frac{-11}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (-6x+2)& = & -10 \color{red}{+} (-7-5x) \\\Leftrightarrow & -18x+6& = &-10-7-5x \\\Leftrightarrow & -18x \color{red}{+6} & = &-17 \color{red}{-5x} \\\Leftrightarrow & -18x \color{red}{+6} \color{blue}{-6} \color{blue}{+5x} & = &-17 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-6} \\\Leftrightarrow & -18x+5x& = &-17-6 \\\Leftrightarrow & -13x& = &-23 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-23}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{23}{13} & & \\ & V = \left\{ \frac{23}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (2x-1)& = & 5 \color{red}{+} (-13-3x) \\\Leftrightarrow & 10x-5& = &5-13-3x \\\Leftrightarrow & 10x \color{red}{-5} & = &-8 \color{red}{-3x} \\\Leftrightarrow & 10x \color{red}{-5} \color{blue}{+5} \color{blue}{+3x} & = &-8 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+5} \\\Leftrightarrow & 10x+3x& = &-8+5 \\\Leftrightarrow & 13x& = &-3 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-3}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-3}{13} & & \\ & V = \left\{ \frac{-3}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (6x-1)& = & -14 \color{red}{+} (-15+x) \\\Leftrightarrow & 18x-3& = &-14-15+x \\\Leftrightarrow & 18x \color{red}{-3} & = &-29 \color{red}{+x} \\\Leftrightarrow & 18x \color{red}{-3} \color{blue}{+3} \color{blue}{-x} & = &-29 \color{red}{+x} \color{blue}{-x} \color{blue}{+3} \\\Leftrightarrow & 18x-x& = &-29+3 \\\Leftrightarrow & 17x& = &-26 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{-26}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{-26}{17} & & \\ & V = \left\{ \frac{-26}{17} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (-2x+1)& = & 9 \color{red}{+} (11-3x) \\\Leftrightarrow & -10x+5& = &9+11-3x \\\Leftrightarrow & -10x \color{red}{+5} & = &20 \color{red}{-3x} \\\Leftrightarrow & -10x \color{red}{+5} \color{blue}{-5} \color{blue}{+3x} & = &20 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-5} \\\Leftrightarrow & -10x+3x& = &20-5 \\\Leftrightarrow & -7x& = &15 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{15}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-15}{7} & & \\ & V = \left\{ \frac{-15}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (6x-1)& = & 13 \color{red}{-} (15+x) \\\Leftrightarrow & 24x-4& = &13-15-x \\\Leftrightarrow & 24x \color{red}{-4} & = &-2 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{-4} \color{blue}{+4} \color{blue}{+x} & = &-2 \color{red}{-x} \color{blue}{+x} \color{blue}{+4} \\\Leftrightarrow & 24x+x& = &-2+4 \\\Leftrightarrow & 25x& = &2 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{2}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{2}{25} & & \\ & V = \left\{ \frac{2}{25} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (-6x+6)& = & -15 \color{red}{+} (-15+x) \\\Leftrightarrow & -30x+30& = &-15-15+x \\\Leftrightarrow & -30x \color{red}{+30} & = &-30 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{+30} \color{blue}{-30} \color{blue}{-x} & = &-30 \color{red}{+x} \color{blue}{-x} \color{blue}{-30} \\\Leftrightarrow & -30x-x& = &-30-30 \\\Leftrightarrow & -31x& = &-60 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{-60}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{60}{31} & & \\ & V = \left\{ \frac{60}{31} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (2x-2)& = & 1 \color{red}{+} (-3-3x) \\\Leftrightarrow & 4x-4& = &1-3-3x \\\Leftrightarrow & 4x \color{red}{-4} & = &-2 \color{red}{-3x} \\\Leftrightarrow & 4x \color{red}{-4} \color{blue}{+4} \color{blue}{+3x} & = &-2 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+4} \\\Leftrightarrow & 4x+3x& = &-2+4 \\\Leftrightarrow & 7x& = &2 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{2}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{2}{7} & & \\ & V = \left\{ \frac{2}{7} \right\} & \\\end{align}\)