Vgln. eerste graad (reeks 3)

Hoofdmenu Eentje per keer  🖨

Reeks met haakjes

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

---

Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (-x+3)& = & -13 \color{red}{-} (-7+x) \\\Leftrightarrow & -2x+6& = &-13+7-x \\\Leftrightarrow & -2x \color{red}{+6} & = &-6 \color{red}{-x} \\\Leftrightarrow & -2x \color{red}{+6} \color{blue}{-6} \color{blue}{+x} & = &-6 \color{red}{-x} \color{blue}{+x} \color{blue}{-6} \\\Leftrightarrow & -2x+x& = &-6-6 \\\Leftrightarrow & -x& = &-12 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-12}{ \color{red}{-1} } \\\Leftrightarrow & x = 12 & & \\ & V = \left\{ 12 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (-4x+6)& = & -7 \color{red}{-} (1+x) \\\Leftrightarrow & -24x+36& = &-7-1-x \\\Leftrightarrow & -24x \color{red}{+36} & = &-8 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{+36} \color{blue}{-36} \color{blue}{+x} & = &-8 \color{red}{-x} \color{blue}{+x} \color{blue}{-36} \\\Leftrightarrow & -24x+x& = &-8-36 \\\Leftrightarrow & -23x& = &-44 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-44}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{44}{23} & & \\ & V = \left\{ \frac{44}{23} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (-6x+4)& = & 8 \color{red}{-} (-1+x) \\\Leftrightarrow & -36x+24& = &8+1-x \\\Leftrightarrow & -36x \color{red}{+24} & = &9 \color{red}{-x} \\\Leftrightarrow & -36x \color{red}{+24} \color{blue}{-24} \color{blue}{+x} & = &9 \color{red}{-x} \color{blue}{+x} \color{blue}{-24} \\\Leftrightarrow & -36x+x& = &9-24 \\\Leftrightarrow & -35x& = &-15 \\\Leftrightarrow & \frac{-35x}{ \color{red}{-35} }& = &\frac{-15}{ \color{red}{-35} } \\\Leftrightarrow & x = \frac{3}{7} & & \\ & V = \left\{ \frac{3}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (4x-6)& = & 15 \color{red}{-} (-14-5x) \\\Leftrightarrow & 8x-12& = &15+14+5x \\\Leftrightarrow & 8x \color{red}{-12} & = &29 \color{red}{+5x} \\\Leftrightarrow & 8x \color{red}{-12} \color{blue}{+12} \color{blue}{-5x} & = &29 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+12} \\\Leftrightarrow & 8x-5x& = &29+12 \\\Leftrightarrow & 3x& = &41 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{41}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{41}{3} & & \\ & V = \left\{ \frac{41}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (5x-5)& = & -3 \color{red}{+} (3+2x) \\\Leftrightarrow & 15x-15& = &-3+3+2x \\\Leftrightarrow & 15x \color{red}{-15} & = &0 \color{red}{+2x} \\\Leftrightarrow & 15x \color{red}{-15} \color{blue}{+15} \color{blue}{-2x} & = &0 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+15} \\\Leftrightarrow & 15x-2x& = &0+15 \\\Leftrightarrow & 13x& = &15 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{15}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{15}{13} & & \\ & V = \left\{ \frac{15}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (5x+3)& = & -10 \color{red}{+} (-7+3x) \\\Leftrightarrow & 20x+12& = &-10-7+3x \\\Leftrightarrow & 20x \color{red}{+12} & = &-17 \color{red}{+3x} \\\Leftrightarrow & 20x \color{red}{+12} \color{blue}{-12} \color{blue}{-3x} & = &-17 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-12} \\\Leftrightarrow & 20x-3x& = &-17-12 \\\Leftrightarrow & 17x& = &-29 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{-29}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{-29}{17} & & \\ & V = \left\{ \frac{-29}{17} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (-5x-7)& = & -12 \color{red}{+} (5+3x) \\\Leftrightarrow & -25x-35& = &-12+5+3x \\\Leftrightarrow & -25x \color{red}{-35} & = &-7 \color{red}{+3x} \\\Leftrightarrow & -25x \color{red}{-35} \color{blue}{+35} \color{blue}{-3x} & = &-7 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+35} \\\Leftrightarrow & -25x-3x& = &-7+35 \\\Leftrightarrow & -28x& = &28 \\\Leftrightarrow & \frac{-28x}{ \color{red}{-28} }& = &\frac{28}{ \color{red}{-28} } \\\Leftrightarrow & x = -1 & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (-2x-1)& = & -15 \color{red}{-} (-13+x) \\\Leftrightarrow & -6x-3& = &-15+13-x \\\Leftrightarrow & -6x \color{red}{-3} & = &-2 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{-3} \color{blue}{+3} \color{blue}{+x} & = &-2 \color{red}{-x} \color{blue}{+x} \color{blue}{+3} \\\Leftrightarrow & -6x+x& = &-2+3 \\\Leftrightarrow & -5x& = &1 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{1}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-1}{5} & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (5x-4)& = & -15 \color{red}{+} (-4-4x) \\\Leftrightarrow & 25x-20& = &-15-4-4x \\\Leftrightarrow & 25x \color{red}{-20} & = &-19 \color{red}{-4x} \\\Leftrightarrow & 25x \color{red}{-20} \color{blue}{+20} \color{blue}{+4x} & = &-19 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+20} \\\Leftrightarrow & 25x+4x& = &-19+20 \\\Leftrightarrow & 29x& = &1 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{1}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{1}{29} & & \\ & V = \left\{ \frac{1}{29} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (-4x-5)& = & 2 \color{red}{+} (-4+x) \\\Leftrightarrow & -16x-20& = &2-4+x \\\Leftrightarrow & -16x \color{red}{-20} & = &-2 \color{red}{+x} \\\Leftrightarrow & -16x \color{red}{-20} \color{blue}{+20} \color{blue}{-x} & = &-2 \color{red}{+x} \color{blue}{-x} \color{blue}{+20} \\\Leftrightarrow & -16x-x& = &-2+20 \\\Leftrightarrow & -17x& = &18 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{18}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{-18}{17} & & \\ & V = \left\{ \frac{-18}{17} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (-x+6)& = & 7 \color{red}{+} (3-5x) \\\Leftrightarrow & -6x+36& = &7+3-5x \\\Leftrightarrow & -6x \color{red}{+36} & = &10 \color{red}{-5x} \\\Leftrightarrow & -6x \color{red}{+36} \color{blue}{-36} \color{blue}{+5x} & = &10 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-36} \\\Leftrightarrow & -6x+5x& = &10-36 \\\Leftrightarrow & -x& = &-26 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-26}{ \color{red}{-1} } \\\Leftrightarrow & x = 26 & & \\ & V = \left\{ 26 \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (-3x+3)& = & 15 \color{red}{+} (-7+x) \\\Leftrightarrow & -12x+12& = &15-7+x \\\Leftrightarrow & -12x \color{red}{+12} & = &8 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &8 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & -12x-x& = &8-12 \\\Leftrightarrow & -13x& = &-4 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-4}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{4}{13} & & \\ & V = \left\{ \frac{4}{13} \right\} & \\\end{align}\)