Vgln. eerste graad (reeks 3)

Hoofdmenu Eentje per keer  🖨

Reeks met haakjes

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

---

Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (-2x-7)& = & -13 \color{red}{+} (14+x) \\\Leftrightarrow & -8x-28& = &-13+14+x \\\Leftrightarrow & -8x \color{red}{-28} & = &1 \color{red}{+x} \\\Leftrightarrow & -8x \color{red}{-28} \color{blue}{+28} \color{blue}{-x} & = &1 \color{red}{+x} \color{blue}{-x} \color{blue}{+28} \\\Leftrightarrow & -8x-x& = &1+28 \\\Leftrightarrow & -9x& = &29 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{29}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{-29}{9} & & \\ & V = \left\{ \frac{-29}{9} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (-5x+2)& = & -10 \color{red}{+} (4+3x) \\\Leftrightarrow & -10x+4& = &-10+4+3x \\\Leftrightarrow & -10x \color{red}{+4} & = &-6 \color{red}{+3x} \\\Leftrightarrow & -10x \color{red}{+4} \color{blue}{-4} \color{blue}{-3x} & = &-6 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-4} \\\Leftrightarrow & -10x-3x& = &-6-4 \\\Leftrightarrow & -13x& = &-10 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-10}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{10}{13} & & \\ & V = \left\{ \frac{10}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (2x-4)& = & -8 \color{red}{-} (11-5x) \\\Leftrightarrow & 8x-16& = &-8-11+5x \\\Leftrightarrow & 8x \color{red}{-16} & = &-19 \color{red}{+5x} \\\Leftrightarrow & 8x \color{red}{-16} \color{blue}{+16} \color{blue}{-5x} & = &-19 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+16} \\\Leftrightarrow & 8x-5x& = &-19+16 \\\Leftrightarrow & 3x& = &-3 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{-3}{ \color{red}{3} } \\\Leftrightarrow & x = -1 & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (-4x+6)& = & 4 \color{red}{-} (-11+x) \\\Leftrightarrow & -20x+30& = &4+11-x \\\Leftrightarrow & -20x \color{red}{+30} & = &15 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{+30} \color{blue}{-30} \color{blue}{+x} & = &15 \color{red}{-x} \color{blue}{+x} \color{blue}{-30} \\\Leftrightarrow & -20x+x& = &15-30 \\\Leftrightarrow & -19x& = &-15 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-15}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{15}{19} & & \\ & V = \left\{ \frac{15}{19} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (-3x+4)& = & 7 \color{red}{+} (-12+x) \\\Leftrightarrow & -6x+8& = &7-12+x \\\Leftrightarrow & -6x \color{red}{+8} & = &-5 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{+8} \color{blue}{-8} \color{blue}{-x} & = &-5 \color{red}{+x} \color{blue}{-x} \color{blue}{-8} \\\Leftrightarrow & -6x-x& = &-5-8 \\\Leftrightarrow & -7x& = &-13 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-13}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{13}{7} & & \\ & V = \left\{ \frac{13}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (-x+2)& = & -7 \color{red}{-} (12-2x) \\\Leftrightarrow & -5x+10& = &-7-12+2x \\\Leftrightarrow & -5x \color{red}{+10} & = &-19 \color{red}{+2x} \\\Leftrightarrow & -5x \color{red}{+10} \color{blue}{-10} \color{blue}{-2x} & = &-19 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-10} \\\Leftrightarrow & -5x-2x& = &-19-10 \\\Leftrightarrow & -7x& = &-29 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-29}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{29}{7} & & \\ & V = \left\{ \frac{29}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (-3x+1)& = & 15 \color{red}{+} (-12+x) \\\Leftrightarrow & -18x+6& = &15-12+x \\\Leftrightarrow & -18x \color{red}{+6} & = &3 \color{red}{+x} \\\Leftrightarrow & -18x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &3 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & -18x-x& = &3-6 \\\Leftrightarrow & -19x& = &-3 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-3}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{3}{19} & & \\ & V = \left\{ \frac{3}{19} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (-x+5)& = & -7 \color{red}{+} (-11+x) \\\Leftrightarrow & -6x+30& = &-7-11+x \\\Leftrightarrow & -6x \color{red}{+30} & = &-18 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{+30} \color{blue}{-30} \color{blue}{-x} & = &-18 \color{red}{+x} \color{blue}{-x} \color{blue}{-30} \\\Leftrightarrow & -6x-x& = &-18-30 \\\Leftrightarrow & -7x& = &-48 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-48}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{48}{7} & & \\ & V = \left\{ \frac{48}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (2x+5)& = & -14 \color{red}{-} (2+x) \\\Leftrightarrow & 12x+30& = &-14-2-x \\\Leftrightarrow & 12x \color{red}{+30} & = &-16 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+30} \color{blue}{-30} \color{blue}{+x} & = &-16 \color{red}{-x} \color{blue}{+x} \color{blue}{-30} \\\Leftrightarrow & 12x+x& = &-16-30 \\\Leftrightarrow & 13x& = &-46 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-46}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-46}{13} & & \\ & V = \left\{ \frac{-46}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (-3x-2)& = & 11 \color{red}{+} (-8-2x) \\\Leftrightarrow & -15x-10& = &11-8-2x \\\Leftrightarrow & -15x \color{red}{-10} & = &3 \color{red}{-2x} \\\Leftrightarrow & -15x \color{red}{-10} \color{blue}{+10} \color{blue}{+2x} & = &3 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+10} \\\Leftrightarrow & -15x+2x& = &3+10 \\\Leftrightarrow & -13x& = &13 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{13}{ \color{red}{-13} } \\\Leftrightarrow & x = -1 & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (-2x-6)& = & -1 \color{red}{-} (-13+x) \\\Leftrightarrow & -12x-36& = &-1+13-x \\\Leftrightarrow & -12x \color{red}{-36} & = &12 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-36} \color{blue}{+36} \color{blue}{+x} & = &12 \color{red}{-x} \color{blue}{+x} \color{blue}{+36} \\\Leftrightarrow & -12x+x& = &12+36 \\\Leftrightarrow & -11x& = &48 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{48}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-48}{11} & & \\ & V = \left\{ \frac{-48}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (-x-2)& = & -14 \color{red}{+} (-11-5x) \\\Leftrightarrow & -6x-12& = &-14-11-5x \\\Leftrightarrow & -6x \color{red}{-12} & = &-25 \color{red}{-5x} \\\Leftrightarrow & -6x \color{red}{-12} \color{blue}{+12} \color{blue}{+5x} & = &-25 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+12} \\\Leftrightarrow & -6x+5x& = &-25+12 \\\Leftrightarrow & -x& = &-13 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-13}{ \color{red}{-1} } \\\Leftrightarrow & x = 13 & & \\ & V = \left\{ 13 \right\} & \\\end{align}\)