Vgln. eerste graad (reeks 3)

Hoofdmenu Eentje per keer  🖨

Reeks met haakjes

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

---

Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (-5x+7)& = & -1 \color{red}{+} (2+x) \\\Leftrightarrow & -15x+21& = &-1+2+x \\\Leftrightarrow & -15x \color{red}{+21} & = &1 \color{red}{+x} \\\Leftrightarrow & -15x \color{red}{+21} \color{blue}{-21} \color{blue}{-x} & = &1 \color{red}{+x} \color{blue}{-x} \color{blue}{-21} \\\Leftrightarrow & -15x-x& = &1-21 \\\Leftrightarrow & -16x& = &-20 \\\Leftrightarrow & \frac{-16x}{ \color{red}{-16} }& = &\frac{-20}{ \color{red}{-16} } \\\Leftrightarrow & x = \frac{5}{4} & & \\ & V = \left\{ \frac{5}{4} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (x+6)& = & 3 \color{red}{-} (12-4x) \\\Leftrightarrow & 5x+30& = &3-12+4x \\\Leftrightarrow & 5x \color{red}{+30} & = &-9 \color{red}{+4x} \\\Leftrightarrow & 5x \color{red}{+30} \color{blue}{-30} \color{blue}{-4x} & = &-9 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-30} \\\Leftrightarrow & 5x-4x& = &-9-30 \\\Leftrightarrow & x& = &-39 \\ & V = \left\{ -39 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (5x+7)& = & -15 \color{red}{+} (-12+x) \\\Leftrightarrow & 25x+35& = &-15-12+x \\\Leftrightarrow & 25x \color{red}{+35} & = &-27 \color{red}{+x} \\\Leftrightarrow & 25x \color{red}{+35} \color{blue}{-35} \color{blue}{-x} & = &-27 \color{red}{+x} \color{blue}{-x} \color{blue}{-35} \\\Leftrightarrow & 25x-x& = &-27-35 \\\Leftrightarrow & 24x& = &-62 \\\Leftrightarrow & \frac{24x}{ \color{red}{24} }& = &\frac{-62}{ \color{red}{24} } \\\Leftrightarrow & x = \frac{-31}{12} & & \\ & V = \left\{ \frac{-31}{12} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (-x+6)& = & 12 \color{red}{-} (2-2x) \\\Leftrightarrow & -3x+18& = &12-2+2x \\\Leftrightarrow & -3x \color{red}{+18} & = &10 \color{red}{+2x} \\\Leftrightarrow & -3x \color{red}{+18} \color{blue}{-18} \color{blue}{-2x} & = &10 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-18} \\\Leftrightarrow & -3x-2x& = &10-18 \\\Leftrightarrow & -5x& = &-8 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-8}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{8}{5} & & \\ & V = \left\{ \frac{8}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (2x-2)& = & -6 \color{red}{+} (13-5x) \\\Leftrightarrow & 6x-6& = &-6+13-5x \\\Leftrightarrow & 6x \color{red}{-6} & = &7 \color{red}{-5x} \\\Leftrightarrow & 6x \color{red}{-6} \color{blue}{+6} \color{blue}{+5x} & = &7 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+6} \\\Leftrightarrow & 6x+5x& = &7+6 \\\Leftrightarrow & 11x& = &13 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{13}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{13}{11} & & \\ & V = \left\{ \frac{13}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (x-3)& = & -15 \color{red}{-} (14-3x) \\\Leftrightarrow & 4x-12& = &-15-14+3x \\\Leftrightarrow & 4x \color{red}{-12} & = &-29 \color{red}{+3x} \\\Leftrightarrow & 4x \color{red}{-12} \color{blue}{+12} \color{blue}{-3x} & = &-29 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+12} \\\Leftrightarrow & 4x-3x& = &-29+12 \\\Leftrightarrow & x& = &-17 \\ & V = \left\{ -17 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (5x-6)& = & 13 \color{red}{-} (3+3x) \\\Leftrightarrow & 20x-24& = &13-3-3x \\\Leftrightarrow & 20x \color{red}{-24} & = &10 \color{red}{-3x} \\\Leftrightarrow & 20x \color{red}{-24} \color{blue}{+24} \color{blue}{+3x} & = &10 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+24} \\\Leftrightarrow & 20x+3x& = &10+24 \\\Leftrightarrow & 23x& = &34 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{34}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{34}{23} & & \\ & V = \left\{ \frac{34}{23} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (-5x-5)& = & -8 \color{red}{+} (13+3x) \\\Leftrightarrow & -10x-10& = &-8+13+3x \\\Leftrightarrow & -10x \color{red}{-10} & = &5 \color{red}{+3x} \\\Leftrightarrow & -10x \color{red}{-10} \color{blue}{+10} \color{blue}{-3x} & = &5 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+10} \\\Leftrightarrow & -10x-3x& = &5+10 \\\Leftrightarrow & -13x& = &15 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{15}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-15}{13} & & \\ & V = \left\{ \frac{-15}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (-4x-2)& = & -15 \color{red}{-} (-10+3x) \\\Leftrightarrow & -16x-8& = &-15+10-3x \\\Leftrightarrow & -16x \color{red}{-8} & = &-5 \color{red}{-3x} \\\Leftrightarrow & -16x \color{red}{-8} \color{blue}{+8} \color{blue}{+3x} & = &-5 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+8} \\\Leftrightarrow & -16x+3x& = &-5+8 \\\Leftrightarrow & -13x& = &3 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{3}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-3}{13} & & \\ & V = \left\{ \frac{-3}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (-2x+4)& = & -3 \color{red}{+} (9+x) \\\Leftrightarrow & -8x+16& = &-3+9+x \\\Leftrightarrow & -8x \color{red}{+16} & = &6 \color{red}{+x} \\\Leftrightarrow & -8x \color{red}{+16} \color{blue}{-16} \color{blue}{-x} & = &6 \color{red}{+x} \color{blue}{-x} \color{blue}{-16} \\\Leftrightarrow & -8x-x& = &6-16 \\\Leftrightarrow & -9x& = &-10 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{-10}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{10}{9} & & \\ & V = \left\{ \frac{10}{9} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (-4x-3)& = & 11 \color{red}{+} (-9+x) \\\Leftrightarrow & -24x-18& = &11-9+x \\\Leftrightarrow & -24x \color{red}{-18} & = &2 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{-18} \color{blue}{+18} \color{blue}{-x} & = &2 \color{red}{+x} \color{blue}{-x} \color{blue}{+18} \\\Leftrightarrow & -24x-x& = &2+18 \\\Leftrightarrow & -25x& = &20 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{20}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{-4}{5} & & \\ & V = \left\{ \frac{-4}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (-5x+2)& = & 7 \color{red}{-} (6+x) \\\Leftrightarrow & -30x+12& = &7-6-x \\\Leftrightarrow & -30x \color{red}{+12} & = &1 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &1 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & -30x+x& = &1-12 \\\Leftrightarrow & -29x& = &-11 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{-11}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{11}{29} & & \\ & V = \left\{ \frac{11}{29} \right\} & \\\end{align}\)