Vgln. eerste graad (reeks 3)

Hoofdmenu Eentje per keer  🖨

Reeks met haakjes

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

---

Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (6x+2)& = & -12 \color{red}{+} (9+x) \\\Leftrightarrow & 18x+6& = &-12+9+x \\\Leftrightarrow & 18x \color{red}{+6} & = &-3 \color{red}{+x} \\\Leftrightarrow & 18x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &-3 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & 18x-x& = &-3-6 \\\Leftrightarrow & 17x& = &-9 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{-9}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{-9}{17} & & \\ & V = \left\{ \frac{-9}{17} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (4x-4)& = & -10 \color{red}{-} (-7+x) \\\Leftrightarrow & 12x-12& = &-10+7-x \\\Leftrightarrow & 12x \color{red}{-12} & = &-3 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &-3 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & 12x+x& = &-3+12 \\\Leftrightarrow & 13x& = &9 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{9}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{9}{13} & & \\ & V = \left\{ \frac{9}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (-4x-6)& = & -3 \color{red}{-} (-2+x) \\\Leftrightarrow & -24x-36& = &-3+2-x \\\Leftrightarrow & -24x \color{red}{-36} & = &-1 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{-36} \color{blue}{+36} \color{blue}{+x} & = &-1 \color{red}{-x} \color{blue}{+x} \color{blue}{+36} \\\Leftrightarrow & -24x+x& = &-1+36 \\\Leftrightarrow & -23x& = &35 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{35}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-35}{23} & & \\ & V = \left\{ \frac{-35}{23} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (-6x-6)& = & -13 \color{red}{+} (11+x) \\\Leftrightarrow & -36x-36& = &-13+11+x \\\Leftrightarrow & -36x \color{red}{-36} & = &-2 \color{red}{+x} \\\Leftrightarrow & -36x \color{red}{-36} \color{blue}{+36} \color{blue}{-x} & = &-2 \color{red}{+x} \color{blue}{-x} \color{blue}{+36} \\\Leftrightarrow & -36x-x& = &-2+36 \\\Leftrightarrow & -37x& = &34 \\\Leftrightarrow & \frac{-37x}{ \color{red}{-37} }& = &\frac{34}{ \color{red}{-37} } \\\Leftrightarrow & x = \frac{-34}{37} & & \\ & V = \left\{ \frac{-34}{37} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (-6x+1)& = & -15 \color{red}{+} (12+x) \\\Leftrightarrow & -18x+3& = &-15+12+x \\\Leftrightarrow & -18x \color{red}{+3} & = &-3 \color{red}{+x} \\\Leftrightarrow & -18x \color{red}{+3} \color{blue}{-3} \color{blue}{-x} & = &-3 \color{red}{+x} \color{blue}{-x} \color{blue}{-3} \\\Leftrightarrow & -18x-x& = &-3-3 \\\Leftrightarrow & -19x& = &-6 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-6}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{6}{19} & & \\ & V = \left\{ \frac{6}{19} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (-4x-1)& = & 14 \color{red}{+} (6+3x) \\\Leftrightarrow & -20x-5& = &14+6+3x \\\Leftrightarrow & -20x \color{red}{-5} & = &20 \color{red}{+3x} \\\Leftrightarrow & -20x \color{red}{-5} \color{blue}{+5} \color{blue}{-3x} & = &20 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+5} \\\Leftrightarrow & -20x-3x& = &20+5 \\\Leftrightarrow & -23x& = &25 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{25}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-25}{23} & & \\ & V = \left\{ \frac{-25}{23} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (-5x-5)& = & 12 \color{red}{-} (-4+2x) \\\Leftrightarrow & -25x-25& = &12+4-2x \\\Leftrightarrow & -25x \color{red}{-25} & = &16 \color{red}{-2x} \\\Leftrightarrow & -25x \color{red}{-25} \color{blue}{+25} \color{blue}{+2x} & = &16 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+25} \\\Leftrightarrow & -25x+2x& = &16+25 \\\Leftrightarrow & -23x& = &41 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{41}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-41}{23} & & \\ & V = \left\{ \frac{-41}{23} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (2x-6)& = & 14 \color{red}{+} (5-3x) \\\Leftrightarrow & 4x-12& = &14+5-3x \\\Leftrightarrow & 4x \color{red}{-12} & = &19 \color{red}{-3x} \\\Leftrightarrow & 4x \color{red}{-12} \color{blue}{+12} \color{blue}{+3x} & = &19 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+12} \\\Leftrightarrow & 4x+3x& = &19+12 \\\Leftrightarrow & 7x& = &31 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{31}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{31}{7} & & \\ & V = \left\{ \frac{31}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (4x-3)& = & -9 \color{red}{+} (-15+x) \\\Leftrightarrow & 24x-18& = &-9-15+x \\\Leftrightarrow & 24x \color{red}{-18} & = &-24 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{-18} \color{blue}{+18} \color{blue}{-x} & = &-24 \color{red}{+x} \color{blue}{-x} \color{blue}{+18} \\\Leftrightarrow & 24x-x& = &-24+18 \\\Leftrightarrow & 23x& = &-6 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-6}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-6}{23} & & \\ & V = \left\{ \frac{-6}{23} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (2x-1)& = & -5 \color{red}{-} (1+x) \\\Leftrightarrow & 8x-4& = &-5-1-x \\\Leftrightarrow & 8x \color{red}{-4} & = &-6 \color{red}{-x} \\\Leftrightarrow & 8x \color{red}{-4} \color{blue}{+4} \color{blue}{+x} & = &-6 \color{red}{-x} \color{blue}{+x} \color{blue}{+4} \\\Leftrightarrow & 8x+x& = &-6+4 \\\Leftrightarrow & 9x& = &-2 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{-2}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{-2}{9} & & \\ & V = \left\{ \frac{-2}{9} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (-3x+5)& = & 12 \color{red}{+} (-5+x) \\\Leftrightarrow & -18x+30& = &12-5+x \\\Leftrightarrow & -18x \color{red}{+30} & = &7 \color{red}{+x} \\\Leftrightarrow & -18x \color{red}{+30} \color{blue}{-30} \color{blue}{-x} & = &7 \color{red}{+x} \color{blue}{-x} \color{blue}{-30} \\\Leftrightarrow & -18x-x& = &7-30 \\\Leftrightarrow & -19x& = &-23 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-23}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{23}{19} & & \\ & V = \left\{ \frac{23}{19} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (-4x+7)& = & 1 \color{red}{+} (11+3x) \\\Leftrightarrow & -16x+28& = &1+11+3x \\\Leftrightarrow & -16x \color{red}{+28} & = &12 \color{red}{+3x} \\\Leftrightarrow & -16x \color{red}{+28} \color{blue}{-28} \color{blue}{-3x} & = &12 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-28} \\\Leftrightarrow & -16x-3x& = &12-28 \\\Leftrightarrow & -19x& = &-16 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-16}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{16}{19} & & \\ & V = \left\{ \frac{16}{19} \right\} & \\\end{align}\)