Vgln. eerste graad (reeks 3)

Hoofdmenu Eentje per keer  🖨

Reeks met haakjes

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

---

Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (-x+4)& = & 11 \color{red}{+} (-7-3x) \\\Leftrightarrow & -4x+16& = &11-7-3x \\\Leftrightarrow & -4x \color{red}{+16} & = &4 \color{red}{-3x} \\\Leftrightarrow & -4x \color{red}{+16} \color{blue}{-16} \color{blue}{+3x} & = &4 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-16} \\\Leftrightarrow & -4x+3x& = &4-16 \\\Leftrightarrow & -x& = &-12 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-12}{ \color{red}{-1} } \\\Leftrightarrow & x = 12 & & \\ & V = \left\{ 12 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (3x+3)& = & -9 \color{red}{-} (9+x) \\\Leftrightarrow & 18x+18& = &-9-9-x \\\Leftrightarrow & 18x \color{red}{+18} & = &-18 \color{red}{-x} \\\Leftrightarrow & 18x \color{red}{+18} \color{blue}{-18} \color{blue}{+x} & = &-18 \color{red}{-x} \color{blue}{+x} \color{blue}{-18} \\\Leftrightarrow & 18x+x& = &-18-18 \\\Leftrightarrow & 19x& = &-36 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-36}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-36}{19} & & \\ & V = \left\{ \frac{-36}{19} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (-2x+4)& = & 1 \color{red}{-} (-14+x) \\\Leftrightarrow & -12x+24& = &1+14-x \\\Leftrightarrow & -12x \color{red}{+24} & = &15 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+24} \color{blue}{-24} \color{blue}{+x} & = &15 \color{red}{-x} \color{blue}{+x} \color{blue}{-24} \\\Leftrightarrow & -12x+x& = &15-24 \\\Leftrightarrow & -11x& = &-9 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-9}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{9}{11} & & \\ & V = \left\{ \frac{9}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (-5x-5)& = & 15 \color{red}{-} (7+x) \\\Leftrightarrow & -30x-30& = &15-7-x \\\Leftrightarrow & -30x \color{red}{-30} & = &8 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{-30} \color{blue}{+30} \color{blue}{+x} & = &8 \color{red}{-x} \color{blue}{+x} \color{blue}{+30} \\\Leftrightarrow & -30x+x& = &8+30 \\\Leftrightarrow & -29x& = &38 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{38}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{-38}{29} & & \\ & V = \left\{ \frac{-38}{29} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (2x-6)& = & -7 \color{red}{-} (11+3x) \\\Leftrightarrow & 8x-24& = &-7-11-3x \\\Leftrightarrow & 8x \color{red}{-24} & = &-18 \color{red}{-3x} \\\Leftrightarrow & 8x \color{red}{-24} \color{blue}{+24} \color{blue}{+3x} & = &-18 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+24} \\\Leftrightarrow & 8x+3x& = &-18+24 \\\Leftrightarrow & 11x& = &6 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{6}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{6}{11} & & \\ & V = \left\{ \frac{6}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (6x+2)& = & 13 \color{red}{-} (6+x) \\\Leftrightarrow & 30x+10& = &13-6-x \\\Leftrightarrow & 30x \color{red}{+10} & = &7 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{+10} \color{blue}{-10} \color{blue}{+x} & = &7 \color{red}{-x} \color{blue}{+x} \color{blue}{-10} \\\Leftrightarrow & 30x+x& = &7-10 \\\Leftrightarrow & 31x& = &-3 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{-3}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{-3}{31} & & \\ & V = \left\{ \frac{-3}{31} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (6x-1)& = & 3 \color{red}{-} (14-5x) \\\Leftrightarrow & 18x-3& = &3-14+5x \\\Leftrightarrow & 18x \color{red}{-3} & = &-11 \color{red}{+5x} \\\Leftrightarrow & 18x \color{red}{-3} \color{blue}{+3} \color{blue}{-5x} & = &-11 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+3} \\\Leftrightarrow & 18x-5x& = &-11+3 \\\Leftrightarrow & 13x& = &-8 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-8}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-8}{13} & & \\ & V = \left\{ \frac{-8}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (-5x+1)& = & -13 \color{red}{-} (-9-2x) \\\Leftrightarrow & -15x+3& = &-13+9+2x \\\Leftrightarrow & -15x \color{red}{+3} & = &-4 \color{red}{+2x} \\\Leftrightarrow & -15x \color{red}{+3} \color{blue}{-3} \color{blue}{-2x} & = &-4 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-3} \\\Leftrightarrow & -15x-2x& = &-4-3 \\\Leftrightarrow & -17x& = &-7 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{-7}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{7}{17} & & \\ & V = \left\{ \frac{7}{17} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (4x-1)& = & 12 \color{red}{-} (-5+x) \\\Leftrightarrow & 20x-5& = &12+5-x \\\Leftrightarrow & 20x \color{red}{-5} & = &17 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{-5} \color{blue}{+5} \color{blue}{+x} & = &17 \color{red}{-x} \color{blue}{+x} \color{blue}{+5} \\\Leftrightarrow & 20x+x& = &17+5 \\\Leftrightarrow & 21x& = &22 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{22}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{22}{21} & & \\ & V = \left\{ \frac{22}{21} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (5x-1)& = & 7 \color{red}{+} (12+x) \\\Leftrightarrow & 15x-3& = &7+12+x \\\Leftrightarrow & 15x \color{red}{-3} & = &19 \color{red}{+x} \\\Leftrightarrow & 15x \color{red}{-3} \color{blue}{+3} \color{blue}{-x} & = &19 \color{red}{+x} \color{blue}{-x} \color{blue}{+3} \\\Leftrightarrow & 15x-x& = &19+3 \\\Leftrightarrow & 14x& = &22 \\\Leftrightarrow & \frac{14x}{ \color{red}{14} }& = &\frac{22}{ \color{red}{14} } \\\Leftrightarrow & x = \frac{11}{7} & & \\ & V = \left\{ \frac{11}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (-x+6)& = & -4 \color{red}{+} (15-5x) \\\Leftrightarrow & -3x+18& = &-4+15-5x \\\Leftrightarrow & -3x \color{red}{+18} & = &11 \color{red}{-5x} \\\Leftrightarrow & -3x \color{red}{+18} \color{blue}{-18} \color{blue}{+5x} & = &11 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-18} \\\Leftrightarrow & -3x+5x& = &11-18 \\\Leftrightarrow & 2x& = &-7 \\\Leftrightarrow & \frac{2x}{ \color{red}{2} }& = &\frac{-7}{ \color{red}{2} } \\\Leftrightarrow & x = \frac{-7}{2} & & \\ & V = \left\{ \frac{-7}{2} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (-2x+6)& = & 12 \color{red}{+} (-7+3x) \\\Leftrightarrow & -8x+24& = &12-7+3x \\\Leftrightarrow & -8x \color{red}{+24} & = &5 \color{red}{+3x} \\\Leftrightarrow & -8x \color{red}{+24} \color{blue}{-24} \color{blue}{-3x} & = &5 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-24} \\\Leftrightarrow & -8x-3x& = &5-24 \\\Leftrightarrow & -11x& = &-19 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-19}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{19}{11} & & \\ & V = \left\{ \frac{19}{11} \right\} & \\\end{align}\)