Vgln. eerste graad (reeks 3)

Hoofdmenu Eentje per keer  🖨

Reeks met haakjes

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

---

Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (-4x+5)& = & 7 \color{red}{-} (1-5x) \\\Leftrightarrow & -8x+10& = &7-1+5x \\\Leftrightarrow & -8x \color{red}{+10} & = &6 \color{red}{+5x} \\\Leftrightarrow & -8x \color{red}{+10} \color{blue}{-10} \color{blue}{-5x} & = &6 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-10} \\\Leftrightarrow & -8x-5x& = &6-10 \\\Leftrightarrow & -13x& = &-4 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-4}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{4}{13} & & \\ & V = \left\{ \frac{4}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (-5x+5)& = & 5 \color{red}{+} (1+x) \\\Leftrightarrow & -20x+20& = &5+1+x \\\Leftrightarrow & -20x \color{red}{+20} & = &6 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{+20} \color{blue}{-20} \color{blue}{-x} & = &6 \color{red}{+x} \color{blue}{-x} \color{blue}{-20} \\\Leftrightarrow & -20x-x& = &6-20 \\\Leftrightarrow & -21x& = &-14 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{-14}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{2}{3} & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (6x-4)& = & 4 \color{red}{+} (14+x) \\\Leftrightarrow & 36x-24& = &4+14+x \\\Leftrightarrow & 36x \color{red}{-24} & = &18 \color{red}{+x} \\\Leftrightarrow & 36x \color{red}{-24} \color{blue}{+24} \color{blue}{-x} & = &18 \color{red}{+x} \color{blue}{-x} \color{blue}{+24} \\\Leftrightarrow & 36x-x& = &18+24 \\\Leftrightarrow & 35x& = &42 \\\Leftrightarrow & \frac{35x}{ \color{red}{35} }& = &\frac{42}{ \color{red}{35} } \\\Leftrightarrow & x = \frac{6}{5} & & \\ & V = \left\{ \frac{6}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (x-1)& = & 4 \color{red}{-} (-15+x) \\\Leftrightarrow & 2x-2& = &4+15-x \\\Leftrightarrow & 2x \color{red}{-2} & = &19 \color{red}{-x} \\\Leftrightarrow & 2x \color{red}{-2} \color{blue}{+2} \color{blue}{+x} & = &19 \color{red}{-x} \color{blue}{+x} \color{blue}{+2} \\\Leftrightarrow & 2x+x& = &19+2 \\\Leftrightarrow & 3x& = &21 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{21}{ \color{red}{3} } \\\Leftrightarrow & x = 7 & & \\ & V = \left\{ 7 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (4x-6)& = & -12 \color{red}{-} (-4+x) \\\Leftrightarrow & 24x-36& = &-12+4-x \\\Leftrightarrow & 24x \color{red}{-36} & = &-8 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{-36} \color{blue}{+36} \color{blue}{+x} & = &-8 \color{red}{-x} \color{blue}{+x} \color{blue}{+36} \\\Leftrightarrow & 24x+x& = &-8+36 \\\Leftrightarrow & 25x& = &28 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{28}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{28}{25} & & \\ & V = \left\{ \frac{28}{25} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (-3x+2)& = & -3 \color{red}{+} (13+x) \\\Leftrightarrow & -18x+12& = &-3+13+x \\\Leftrightarrow & -18x \color{red}{+12} & = &10 \color{red}{+x} \\\Leftrightarrow & -18x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &10 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & -18x-x& = &10-12 \\\Leftrightarrow & -19x& = &-2 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-2}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{2}{19} & & \\ & V = \left\{ \frac{2}{19} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (-3x-5)& = & 4 \color{red}{+} (3-2x) \\\Leftrightarrow & -9x-15& = &4+3-2x \\\Leftrightarrow & -9x \color{red}{-15} & = &7 \color{red}{-2x} \\\Leftrightarrow & -9x \color{red}{-15} \color{blue}{+15} \color{blue}{+2x} & = &7 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+15} \\\Leftrightarrow & -9x+2x& = &7+15 \\\Leftrightarrow & -7x& = &22 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{22}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-22}{7} & & \\ & V = \left\{ \frac{-22}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (2x+2)& = & -7 \color{red}{+} (-7+x) \\\Leftrightarrow & 6x+6& = &-7-7+x \\\Leftrightarrow & 6x \color{red}{+6} & = &-14 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &-14 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & 6x-x& = &-14-6 \\\Leftrightarrow & 5x& = &-20 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-20}{ \color{red}{5} } \\\Leftrightarrow & x = -4 & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (-5x-3)& = & -13 \color{red}{+} (-12+3x) \\\Leftrightarrow & -25x-15& = &-13-12+3x \\\Leftrightarrow & -25x \color{red}{-15} & = &-25 \color{red}{+3x} \\\Leftrightarrow & -25x \color{red}{-15} \color{blue}{+15} \color{blue}{-3x} & = &-25 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+15} \\\Leftrightarrow & -25x-3x& = &-25+15 \\\Leftrightarrow & -28x& = &-10 \\\Leftrightarrow & \frac{-28x}{ \color{red}{-28} }& = &\frac{-10}{ \color{red}{-28} } \\\Leftrightarrow & x = \frac{5}{14} & & \\ & V = \left\{ \frac{5}{14} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (-6x+2)& = & 13 \color{red}{+} (-8-5x) \\\Leftrightarrow & -36x+12& = &13-8-5x \\\Leftrightarrow & -36x \color{red}{+12} & = &5 \color{red}{-5x} \\\Leftrightarrow & -36x \color{red}{+12} \color{blue}{-12} \color{blue}{+5x} & = &5 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-12} \\\Leftrightarrow & -36x+5x& = &5-12 \\\Leftrightarrow & -31x& = &-7 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{-7}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{7}{31} & & \\ & V = \left\{ \frac{7}{31} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (5x+3)& = & 9 \color{red}{-} (8+x) \\\Leftrightarrow & 30x+18& = &9-8-x \\\Leftrightarrow & 30x \color{red}{+18} & = &1 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{+18} \color{blue}{-18} \color{blue}{+x} & = &1 \color{red}{-x} \color{blue}{+x} \color{blue}{-18} \\\Leftrightarrow & 30x+x& = &1-18 \\\Leftrightarrow & 31x& = &-17 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{-17}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{-17}{31} & & \\ & V = \left\{ \frac{-17}{31} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (5x-7)& = & -6 \color{red}{+} (2-3x) \\\Leftrightarrow & 10x-14& = &-6+2-3x \\\Leftrightarrow & 10x \color{red}{-14} & = &-4 \color{red}{-3x} \\\Leftrightarrow & 10x \color{red}{-14} \color{blue}{+14} \color{blue}{+3x} & = &-4 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+14} \\\Leftrightarrow & 10x+3x& = &-4+14 \\\Leftrightarrow & 13x& = &10 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{10}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{10}{13} & & \\ & V = \left\{ \frac{10}{13} \right\} & \\\end{align}\)