Vgln. eerste graad (reeks 3)

Hoofdmenu Eentje per keer  🖨

Reeks met haakjes

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

---

Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (-5x+4)& = & -6 \color{red}{+} (7+x) \\\Leftrightarrow & -30x+24& = &-6+7+x \\\Leftrightarrow & -30x \color{red}{+24} & = &1 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{+24} \color{blue}{-24} \color{blue}{-x} & = &1 \color{red}{+x} \color{blue}{-x} \color{blue}{-24} \\\Leftrightarrow & -30x-x& = &1-24 \\\Leftrightarrow & -31x& = &-23 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{-23}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{23}{31} & & \\ & V = \left\{ \frac{23}{31} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (-x+2)& = & 15 \color{red}{-} (2-2x) \\\Leftrightarrow & -3x+6& = &15-2+2x \\\Leftrightarrow & -3x \color{red}{+6} & = &13 \color{red}{+2x} \\\Leftrightarrow & -3x \color{red}{+6} \color{blue}{-6} \color{blue}{-2x} & = &13 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-6} \\\Leftrightarrow & -3x-2x& = &13-6 \\\Leftrightarrow & -5x& = &7 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{7}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-7}{5} & & \\ & V = \left\{ \frac{-7}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (6x-4)& = & 11 \color{red}{-} (-3+x) \\\Leftrightarrow & 18x-12& = &11+3-x \\\Leftrightarrow & 18x \color{red}{-12} & = &14 \color{red}{-x} \\\Leftrightarrow & 18x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &14 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & 18x+x& = &14+12 \\\Leftrightarrow & 19x& = &26 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{26}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{26}{19} & & \\ & V = \left\{ \frac{26}{19} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (x+4)& = & 12 \color{red}{-} (-11+x) \\\Leftrightarrow & 3x+12& = &12+11-x \\\Leftrightarrow & 3x \color{red}{+12} & = &23 \color{red}{-x} \\\Leftrightarrow & 3x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &23 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & 3x+x& = &23-12 \\\Leftrightarrow & 4x& = &11 \\\Leftrightarrow & \frac{4x}{ \color{red}{4} }& = &\frac{11}{ \color{red}{4} } \\\Leftrightarrow & x = \frac{11}{4} & & \\ & V = \left\{ \frac{11}{4} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (-4x+5)& = & -15 \color{red}{+} (-8+x) \\\Leftrightarrow & -24x+30& = &-15-8+x \\\Leftrightarrow & -24x \color{red}{+30} & = &-23 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{+30} \color{blue}{-30} \color{blue}{-x} & = &-23 \color{red}{+x} \color{blue}{-x} \color{blue}{-30} \\\Leftrightarrow & -24x-x& = &-23-30 \\\Leftrightarrow & -25x& = &-53 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{-53}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{53}{25} & & \\ & V = \left\{ \frac{53}{25} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (-x+1)& = & -15 \color{red}{-} (4+3x) \\\Leftrightarrow & -4x+4& = &-15-4-3x \\\Leftrightarrow & -4x \color{red}{+4} & = &-19 \color{red}{-3x} \\\Leftrightarrow & -4x \color{red}{+4} \color{blue}{-4} \color{blue}{+3x} & = &-19 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-4} \\\Leftrightarrow & -4x+3x& = &-19-4 \\\Leftrightarrow & -x& = &-23 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-23}{ \color{red}{-1} } \\\Leftrightarrow & x = 23 & & \\ & V = \left\{ 23 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (-5x-2)& = & 1 \color{red}{+} (11+x) \\\Leftrightarrow & -20x-8& = &1+11+x \\\Leftrightarrow & -20x \color{red}{-8} & = &12 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{-8} \color{blue}{+8} \color{blue}{-x} & = &12 \color{red}{+x} \color{blue}{-x} \color{blue}{+8} \\\Leftrightarrow & -20x-x& = &12+8 \\\Leftrightarrow & -21x& = &20 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{20}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{-20}{21} & & \\ & V = \left\{ \frac{-20}{21} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (-x-5)& = & 6 \color{red}{-} (-15-3x) \\\Leftrightarrow & -4x-20& = &6+15+3x \\\Leftrightarrow & -4x \color{red}{-20} & = &21 \color{red}{+3x} \\\Leftrightarrow & -4x \color{red}{-20} \color{blue}{+20} \color{blue}{-3x} & = &21 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+20} \\\Leftrightarrow & -4x-3x& = &21+20 \\\Leftrightarrow & -7x& = &41 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{41}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-41}{7} & & \\ & V = \left\{ \frac{-41}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (-x+1)& = & 7 \color{red}{+} (12+x) \\\Leftrightarrow & -6x+6& = &7+12+x \\\Leftrightarrow & -6x \color{red}{+6} & = &19 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &19 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & -6x-x& = &19-6 \\\Leftrightarrow & -7x& = &13 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{13}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-13}{7} & & \\ & V = \left\{ \frac{-13}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (-6x-7)& = & 6 \color{red}{-} (6+x) \\\Leftrightarrow & -24x-28& = &6-6-x \\\Leftrightarrow & -24x \color{red}{-28} & = &0 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{-28} \color{blue}{+28} \color{blue}{+x} & = &0 \color{red}{-x} \color{blue}{+x} \color{blue}{+28} \\\Leftrightarrow & -24x+x& = &0+28 \\\Leftrightarrow & -23x& = &28 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{28}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-28}{23} & & \\ & V = \left\{ \frac{-28}{23} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (-5x+2)& = & -10 \color{red}{-} (-12+x) \\\Leftrightarrow & -25x+10& = &-10+12-x \\\Leftrightarrow & -25x \color{red}{+10} & = &2 \color{red}{-x} \\\Leftrightarrow & -25x \color{red}{+10} \color{blue}{-10} \color{blue}{+x} & = &2 \color{red}{-x} \color{blue}{+x} \color{blue}{-10} \\\Leftrightarrow & -25x+x& = &2-10 \\\Leftrightarrow & -24x& = &-8 \\\Leftrightarrow & \frac{-24x}{ \color{red}{-24} }& = &\frac{-8}{ \color{red}{-24} } \\\Leftrightarrow & x = \frac{1}{3} & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (x+3)& = & -7 \color{red}{-} (-3+x) \\\Leftrightarrow & 6x+18& = &-7+3-x \\\Leftrightarrow & 6x \color{red}{+18} & = &-4 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{+18} \color{blue}{-18} \color{blue}{+x} & = &-4 \color{red}{-x} \color{blue}{+x} \color{blue}{-18} \\\Leftrightarrow & 6x+x& = &-4-18 \\\Leftrightarrow & 7x& = &-22 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-22}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-22}{7} & & \\ & V = \left\{ \frac{-22}{7} \right\} & \\\end{align}\)