Vgln. eerste graad (reeks 3)

Hoofdmenu Eentje per keer  🖨

Reeks met haakjes

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

---

Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (5x-5)& = & 12 \color{red}{+} (-1+x) \\\Leftrightarrow & 30x-30& = &12-1+x \\\Leftrightarrow & 30x \color{red}{-30} & = &11 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{-30} \color{blue}{+30} \color{blue}{-x} & = &11 \color{red}{+x} \color{blue}{-x} \color{blue}{+30} \\\Leftrightarrow & 30x-x& = &11+30 \\\Leftrightarrow & 29x& = &41 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{41}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{41}{29} & & \\ & V = \left\{ \frac{41}{29} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (5x-1)& = & -8 \color{red}{-} (-6+x) \\\Leftrightarrow & 30x-6& = &-8+6-x \\\Leftrightarrow & 30x \color{red}{-6} & = &-2 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &-2 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & 30x+x& = &-2+6 \\\Leftrightarrow & 31x& = &4 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{4}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{4}{31} & & \\ & V = \left\{ \frac{4}{31} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (-6x+2)& = & 3 \color{red}{+} (-1-5x) \\\Leftrightarrow & -18x+6& = &3-1-5x \\\Leftrightarrow & -18x \color{red}{+6} & = &2 \color{red}{-5x} \\\Leftrightarrow & -18x \color{red}{+6} \color{blue}{-6} \color{blue}{+5x} & = &2 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-6} \\\Leftrightarrow & -18x+5x& = &2-6 \\\Leftrightarrow & -13x& = &-4 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-4}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{4}{13} & & \\ & V = \left\{ \frac{4}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (5x-6)& = & 9 \color{red}{+} (9+3x) \\\Leftrightarrow & 25x-30& = &9+9+3x \\\Leftrightarrow & 25x \color{red}{-30} & = &18 \color{red}{+3x} \\\Leftrightarrow & 25x \color{red}{-30} \color{blue}{+30} \color{blue}{-3x} & = &18 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+30} \\\Leftrightarrow & 25x-3x& = &18+30 \\\Leftrightarrow & 22x& = &48 \\\Leftrightarrow & \frac{22x}{ \color{red}{22} }& = &\frac{48}{ \color{red}{22} } \\\Leftrightarrow & x = \frac{24}{11} & & \\ & V = \left\{ \frac{24}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (3x+1)& = & -4 \color{red}{+} (15-2x) \\\Leftrightarrow & 15x+5& = &-4+15-2x \\\Leftrightarrow & 15x \color{red}{+5} & = &11 \color{red}{-2x} \\\Leftrightarrow & 15x \color{red}{+5} \color{blue}{-5} \color{blue}{+2x} & = &11 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-5} \\\Leftrightarrow & 15x+2x& = &11-5 \\\Leftrightarrow & 17x& = &6 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{6}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{6}{17} & & \\ & V = \left\{ \frac{6}{17} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (-x-4)& = & -8 \color{red}{-} (15-2x) \\\Leftrightarrow & -5x-20& = &-8-15+2x \\\Leftrightarrow & -5x \color{red}{-20} & = &-23 \color{red}{+2x} \\\Leftrightarrow & -5x \color{red}{-20} \color{blue}{+20} \color{blue}{-2x} & = &-23 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+20} \\\Leftrightarrow & -5x-2x& = &-23+20 \\\Leftrightarrow & -7x& = &-3 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-3}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{3}{7} & & \\ & V = \left\{ \frac{3}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (-2x+4)& = & 13 \color{red}{-} (5-5x) \\\Leftrightarrow & -6x+12& = &13-5+5x \\\Leftrightarrow & -6x \color{red}{+12} & = &8 \color{red}{+5x} \\\Leftrightarrow & -6x \color{red}{+12} \color{blue}{-12} \color{blue}{-5x} & = &8 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-12} \\\Leftrightarrow & -6x-5x& = &8-12 \\\Leftrightarrow & -11x& = &-4 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-4}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{4}{11} & & \\ & V = \left\{ \frac{4}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (4x-7)& = & 10 \color{red}{-} (2+x) \\\Leftrightarrow & 24x-42& = &10-2-x \\\Leftrightarrow & 24x \color{red}{-42} & = &8 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{-42} \color{blue}{+42} \color{blue}{+x} & = &8 \color{red}{-x} \color{blue}{+x} \color{blue}{+42} \\\Leftrightarrow & 24x+x& = &8+42 \\\Leftrightarrow & 25x& = &50 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{50}{ \color{red}{25} } \\\Leftrightarrow & x = 2 & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (2x+7)& = & 11 \color{red}{-} (-4+x) \\\Leftrightarrow & 8x+28& = &11+4-x \\\Leftrightarrow & 8x \color{red}{+28} & = &15 \color{red}{-x} \\\Leftrightarrow & 8x \color{red}{+28} \color{blue}{-28} \color{blue}{+x} & = &15 \color{red}{-x} \color{blue}{+x} \color{blue}{-28} \\\Leftrightarrow & 8x+x& = &15-28 \\\Leftrightarrow & 9x& = &-13 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{-13}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{-13}{9} & & \\ & V = \left\{ \frac{-13}{9} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (6x-6)& = & -2 \color{red}{-} (-1+x) \\\Leftrightarrow & 30x-30& = &-2+1-x \\\Leftrightarrow & 30x \color{red}{-30} & = &-1 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{-30} \color{blue}{+30} \color{blue}{+x} & = &-1 \color{red}{-x} \color{blue}{+x} \color{blue}{+30} \\\Leftrightarrow & 30x+x& = &-1+30 \\\Leftrightarrow & 31x& = &29 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{29}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{29}{31} & & \\ & V = \left\{ \frac{29}{31} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (-2x-1)& = & 5 \color{red}{+} (-11-5x) \\\Leftrightarrow & -6x-3& = &5-11-5x \\\Leftrightarrow & -6x \color{red}{-3} & = &-6 \color{red}{-5x} \\\Leftrightarrow & -6x \color{red}{-3} \color{blue}{+3} \color{blue}{+5x} & = &-6 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+3} \\\Leftrightarrow & -6x+5x& = &-6+3 \\\Leftrightarrow & -x& = &-3 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-3}{ \color{red}{-1} } \\\Leftrightarrow & x = 3 & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (5x+4)& = & 10 \color{red}{+} (-5+4x) \\\Leftrightarrow & 25x+20& = &10-5+4x \\\Leftrightarrow & 25x \color{red}{+20} & = &5 \color{red}{+4x} \\\Leftrightarrow & 25x \color{red}{+20} \color{blue}{-20} \color{blue}{-4x} & = &5 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-20} \\\Leftrightarrow & 25x-4x& = &5-20 \\\Leftrightarrow & 21x& = &-15 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{-15}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{-5}{7} & & \\ & V = \left\{ \frac{-5}{7} \right\} & \\\end{align}\)