Vgln. eerste graad (reeks 3)

Hoofdmenu Eentje per keer  🖨

Reeks met haakjes

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

---

Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (-x+6)& = & 9 \color{red}{-} (4+3x) \\\Leftrightarrow & -4x+24& = &9-4-3x \\\Leftrightarrow & -4x \color{red}{+24} & = &5 \color{red}{-3x} \\\Leftrightarrow & -4x \color{red}{+24} \color{blue}{-24} \color{blue}{+3x} & = &5 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-24} \\\Leftrightarrow & -4x+3x& = &5-24 \\\Leftrightarrow & -x& = &-19 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-19}{ \color{red}{-1} } \\\Leftrightarrow & x = 19 & & \\ & V = \left\{ 19 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (4x+2)& = & -15 \color{red}{+} (12+x) \\\Leftrightarrow & 12x+6& = &-15+12+x \\\Leftrightarrow & 12x \color{red}{+6} & = &-3 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &-3 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & 12x-x& = &-3-6 \\\Leftrightarrow & 11x& = &-9 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-9}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-9}{11} & & \\ & V = \left\{ \frac{-9}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (-3x-2)& = & -8 \color{red}{+} (-5+x) \\\Leftrightarrow & -18x-12& = &-8-5+x \\\Leftrightarrow & -18x \color{red}{-12} & = &-13 \color{red}{+x} \\\Leftrightarrow & -18x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &-13 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & -18x-x& = &-13+12 \\\Leftrightarrow & -19x& = &-1 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-1}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{1}{19} & & \\ & V = \left\{ \frac{1}{19} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (6x+1)& = & 11 \color{red}{-} (-5+x) \\\Leftrightarrow & 12x+2& = &11+5-x \\\Leftrightarrow & 12x \color{red}{+2} & = &16 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+2} \color{blue}{-2} \color{blue}{+x} & = &16 \color{red}{-x} \color{blue}{+x} \color{blue}{-2} \\\Leftrightarrow & 12x+x& = &16-2 \\\Leftrightarrow & 13x& = &14 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{14}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{14}{13} & & \\ & V = \left\{ \frac{14}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (-5x+7)& = & -7 \color{red}{+} (8+x) \\\Leftrightarrow & -25x+35& = &-7+8+x \\\Leftrightarrow & -25x \color{red}{+35} & = &1 \color{red}{+x} \\\Leftrightarrow & -25x \color{red}{+35} \color{blue}{-35} \color{blue}{-x} & = &1 \color{red}{+x} \color{blue}{-x} \color{blue}{-35} \\\Leftrightarrow & -25x-x& = &1-35 \\\Leftrightarrow & -26x& = &-34 \\\Leftrightarrow & \frac{-26x}{ \color{red}{-26} }& = &\frac{-34}{ \color{red}{-26} } \\\Leftrightarrow & x = \frac{17}{13} & & \\ & V = \left\{ \frac{17}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (-2x-6)& = & 5 \color{red}{-} (11-5x) \\\Leftrightarrow & -6x-18& = &5-11+5x \\\Leftrightarrow & -6x \color{red}{-18} & = &-6 \color{red}{+5x} \\\Leftrightarrow & -6x \color{red}{-18} \color{blue}{+18} \color{blue}{-5x} & = &-6 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+18} \\\Leftrightarrow & -6x-5x& = &-6+18 \\\Leftrightarrow & -11x& = &12 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{12}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-12}{11} & & \\ & V = \left\{ \frac{-12}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (2x-5)& = & -11 \color{red}{+} (-5+x) \\\Leftrightarrow & 10x-25& = &-11-5+x \\\Leftrightarrow & 10x \color{red}{-25} & = &-16 \color{red}{+x} \\\Leftrightarrow & 10x \color{red}{-25} \color{blue}{+25} \color{blue}{-x} & = &-16 \color{red}{+x} \color{blue}{-x} \color{blue}{+25} \\\Leftrightarrow & 10x-x& = &-16+25 \\\Leftrightarrow & 9x& = &9 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{9}{ \color{red}{9} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (6x+6)& = & -15 \color{red}{-} (15+x) \\\Leftrightarrow & 24x+24& = &-15-15-x \\\Leftrightarrow & 24x \color{red}{+24} & = &-30 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{+24} \color{blue}{-24} \color{blue}{+x} & = &-30 \color{red}{-x} \color{blue}{+x} \color{blue}{-24} \\\Leftrightarrow & 24x+x& = &-30-24 \\\Leftrightarrow & 25x& = &-54 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{-54}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{-54}{25} & & \\ & V = \left\{ \frac{-54}{25} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (-2x+1)& = & -14 \color{red}{-} (-7-3x) \\\Leftrightarrow & -4x+2& = &-14+7+3x \\\Leftrightarrow & -4x \color{red}{+2} & = &-7 \color{red}{+3x} \\\Leftrightarrow & -4x \color{red}{+2} \color{blue}{-2} \color{blue}{-3x} & = &-7 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-2} \\\Leftrightarrow & -4x-3x& = &-7-2 \\\Leftrightarrow & -7x& = &-9 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-9}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{9}{7} & & \\ & V = \left\{ \frac{9}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (4x+4)& = & -1 \color{red}{-} (2+3x) \\\Leftrightarrow & 16x+16& = &-1-2-3x \\\Leftrightarrow & 16x \color{red}{+16} & = &-3 \color{red}{-3x} \\\Leftrightarrow & 16x \color{red}{+16} \color{blue}{-16} \color{blue}{+3x} & = &-3 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-16} \\\Leftrightarrow & 16x+3x& = &-3-16 \\\Leftrightarrow & 19x& = &-19 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-19}{ \color{red}{19} } \\\Leftrightarrow & x = -1 & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (3x+4)& = & -8 \color{red}{+} (-12+x) \\\Leftrightarrow & 6x+8& = &-8-12+x \\\Leftrightarrow & 6x \color{red}{+8} & = &-20 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{+8} \color{blue}{-8} \color{blue}{-x} & = &-20 \color{red}{+x} \color{blue}{-x} \color{blue}{-8} \\\Leftrightarrow & 6x-x& = &-20-8 \\\Leftrightarrow & 5x& = &-28 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-28}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{-28}{5} & & \\ & V = \left\{ \frac{-28}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (x+3)& = & -11 \color{red}{-} (3+x) \\\Leftrightarrow & 2x+6& = &-11-3-x \\\Leftrightarrow & 2x \color{red}{+6} & = &-14 \color{red}{-x} \\\Leftrightarrow & 2x \color{red}{+6} \color{blue}{-6} \color{blue}{+x} & = &-14 \color{red}{-x} \color{blue}{+x} \color{blue}{-6} \\\Leftrightarrow & 2x+x& = &-14-6 \\\Leftrightarrow & 3x& = &-20 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{-20}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{-20}{3} & & \\ & V = \left\{ \frac{-20}{3} \right\} & \\\end{align}\)