Vgln. eerste graad (reeks 3)

Hoofdmenu Eentje per keer  🖨

Reeks met haakjes

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

---

Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (3x+6)& = & -4 \color{red}{-} (1+x) \\\Leftrightarrow & 12x+24& = &-4-1-x \\\Leftrightarrow & 12x \color{red}{+24} & = &-5 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+24} \color{blue}{-24} \color{blue}{+x} & = &-5 \color{red}{-x} \color{blue}{+x} \color{blue}{-24} \\\Leftrightarrow & 12x+x& = &-5-24 \\\Leftrightarrow & 13x& = &-29 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-29}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-29}{13} & & \\ & V = \left\{ \frac{-29}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (3x-6)& = & 9 \color{red}{-} (-7+x) \\\Leftrightarrow & 12x-24& = &9+7-x \\\Leftrightarrow & 12x \color{red}{-24} & = &16 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-24} \color{blue}{+24} \color{blue}{+x} & = &16 \color{red}{-x} \color{blue}{+x} \color{blue}{+24} \\\Leftrightarrow & 12x+x& = &16+24 \\\Leftrightarrow & 13x& = &40 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{40}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{40}{13} & & \\ & V = \left\{ \frac{40}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (-4x-1)& = & -5 \color{red}{+} (-4+x) \\\Leftrightarrow & -20x-5& = &-5-4+x \\\Leftrightarrow & -20x \color{red}{-5} & = &-9 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{-5} \color{blue}{+5} \color{blue}{-x} & = &-9 \color{red}{+x} \color{blue}{-x} \color{blue}{+5} \\\Leftrightarrow & -20x-x& = &-9+5 \\\Leftrightarrow & -21x& = &-4 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{-4}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{4}{21} & & \\ & V = \left\{ \frac{4}{21} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (-x+3)& = & 3 \color{red}{-} (15+4x) \\\Leftrightarrow & -5x+15& = &3-15-4x \\\Leftrightarrow & -5x \color{red}{+15} & = &-12 \color{red}{-4x} \\\Leftrightarrow & -5x \color{red}{+15} \color{blue}{-15} \color{blue}{+4x} & = &-12 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-15} \\\Leftrightarrow & -5x+4x& = &-12-15 \\\Leftrightarrow & -x& = &-27 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-27}{ \color{red}{-1} } \\\Leftrightarrow & x = 27 & & \\ & V = \left\{ 27 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (2x+3)& = & -1 \color{red}{+} (-8+x) \\\Leftrightarrow & 10x+15& = &-1-8+x \\\Leftrightarrow & 10x \color{red}{+15} & = &-9 \color{red}{+x} \\\Leftrightarrow & 10x \color{red}{+15} \color{blue}{-15} \color{blue}{-x} & = &-9 \color{red}{+x} \color{blue}{-x} \color{blue}{-15} \\\Leftrightarrow & 10x-x& = &-9-15 \\\Leftrightarrow & 9x& = &-24 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{-24}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{-8}{3} & & \\ & V = \left\{ \frac{-8}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (-3x-1)& = & 9 \color{red}{+} (-12-2x) \\\Leftrightarrow & -9x-3& = &9-12-2x \\\Leftrightarrow & -9x \color{red}{-3} & = &-3 \color{red}{-2x} \\\Leftrightarrow & -9x \color{red}{-3} \color{blue}{+3} \color{blue}{+2x} & = &-3 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+3} \\\Leftrightarrow & -9x+2x& = &-3+3 \\\Leftrightarrow & -7x& = &0 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{0}{ \color{red}{-7} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (-2x+3)& = & -11 \color{red}{-} (-4+x) \\\Leftrightarrow & -4x+6& = &-11+4-x \\\Leftrightarrow & -4x \color{red}{+6} & = &-7 \color{red}{-x} \\\Leftrightarrow & -4x \color{red}{+6} \color{blue}{-6} \color{blue}{+x} & = &-7 \color{red}{-x} \color{blue}{+x} \color{blue}{-6} \\\Leftrightarrow & -4x+x& = &-7-6 \\\Leftrightarrow & -3x& = &-13 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{-13}{ \color{red}{-3} } \\\Leftrightarrow & x = \frac{13}{3} & & \\ & V = \left\{ \frac{13}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (-6x+5)& = & -7 \color{red}{-} (-13-5x) \\\Leftrightarrow & -18x+15& = &-7+13+5x \\\Leftrightarrow & -18x \color{red}{+15} & = &6 \color{red}{+5x} \\\Leftrightarrow & -18x \color{red}{+15} \color{blue}{-15} \color{blue}{-5x} & = &6 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-15} \\\Leftrightarrow & -18x-5x& = &6-15 \\\Leftrightarrow & -23x& = &-9 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-9}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{9}{23} & & \\ & V = \left\{ \frac{9}{23} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (5x+3)& = & -11 \color{red}{+} (-6+x) \\\Leftrightarrow & 25x+15& = &-11-6+x \\\Leftrightarrow & 25x \color{red}{+15} & = &-17 \color{red}{+x} \\\Leftrightarrow & 25x \color{red}{+15} \color{blue}{-15} \color{blue}{-x} & = &-17 \color{red}{+x} \color{blue}{-x} \color{blue}{-15} \\\Leftrightarrow & 25x-x& = &-17-15 \\\Leftrightarrow & 24x& = &-32 \\\Leftrightarrow & \frac{24x}{ \color{red}{24} }& = &\frac{-32}{ \color{red}{24} } \\\Leftrightarrow & x = \frac{-4}{3} & & \\ & V = \left\{ \frac{-4}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (-x+4)& = & -9 \color{red}{+} (-11+x) \\\Leftrightarrow & -2x+8& = &-9-11+x \\\Leftrightarrow & -2x \color{red}{+8} & = &-20 \color{red}{+x} \\\Leftrightarrow & -2x \color{red}{+8} \color{blue}{-8} \color{blue}{-x} & = &-20 \color{red}{+x} \color{blue}{-x} \color{blue}{-8} \\\Leftrightarrow & -2x-x& = &-20-8 \\\Leftrightarrow & -3x& = &-28 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{-28}{ \color{red}{-3} } \\\Leftrightarrow & x = \frac{28}{3} & & \\ & V = \left\{ \frac{28}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (4x-2)& = & -6 \color{red}{-} (2+x) \\\Leftrightarrow & 20x-10& = &-6-2-x \\\Leftrightarrow & 20x \color{red}{-10} & = &-8 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{-10} \color{blue}{+10} \color{blue}{+x} & = &-8 \color{red}{-x} \color{blue}{+x} \color{blue}{+10} \\\Leftrightarrow & 20x+x& = &-8+10 \\\Leftrightarrow & 21x& = &2 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{2}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{2}{21} & & \\ & V = \left\{ \frac{2}{21} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (6x+7)& = & 9 \color{red}{+} (1+x) \\\Leftrightarrow & 24x+28& = &9+1+x \\\Leftrightarrow & 24x \color{red}{+28} & = &10 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{+28} \color{blue}{-28} \color{blue}{-x} & = &10 \color{red}{+x} \color{blue}{-x} \color{blue}{-28} \\\Leftrightarrow & 24x-x& = &10-28 \\\Leftrightarrow & 23x& = &-18 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-18}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-18}{23} & & \\ & V = \left\{ \frac{-18}{23} \right\} & \\\end{align}\)