Vgln. eerste graad (reeks 3)

Hoofdmenu Eentje per keer  🖨

Reeks met haakjes

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

---

Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (5x-3)& = & 5 \color{red}{-} (-12+x) \\\Leftrightarrow & 25x-15& = &5+12-x \\\Leftrightarrow & 25x \color{red}{-15} & = &17 \color{red}{-x} \\\Leftrightarrow & 25x \color{red}{-15} \color{blue}{+15} \color{blue}{+x} & = &17 \color{red}{-x} \color{blue}{+x} \color{blue}{+15} \\\Leftrightarrow & 25x+x& = &17+15 \\\Leftrightarrow & 26x& = &32 \\\Leftrightarrow & \frac{26x}{ \color{red}{26} }& = &\frac{32}{ \color{red}{26} } \\\Leftrightarrow & x = \frac{16}{13} & & \\ & V = \left\{ \frac{16}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (-4x+6)& = & 12 \color{red}{-} (10+x) \\\Leftrightarrow & -12x+18& = &12-10-x \\\Leftrightarrow & -12x \color{red}{+18} & = &2 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+18} \color{blue}{-18} \color{blue}{+x} & = &2 \color{red}{-x} \color{blue}{+x} \color{blue}{-18} \\\Leftrightarrow & -12x+x& = &2-18 \\\Leftrightarrow & -11x& = &-16 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-16}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{16}{11} & & \\ & V = \left\{ \frac{16}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (4x-7)& = & 13 \color{red}{+} (15+3x) \\\Leftrightarrow & 20x-35& = &13+15+3x \\\Leftrightarrow & 20x \color{red}{-35} & = &28 \color{red}{+3x} \\\Leftrightarrow & 20x \color{red}{-35} \color{blue}{+35} \color{blue}{-3x} & = &28 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+35} \\\Leftrightarrow & 20x-3x& = &28+35 \\\Leftrightarrow & 17x& = &63 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{63}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{63}{17} & & \\ & V = \left\{ \frac{63}{17} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (-2x-1)& = & -1 \color{red}{-} (-7+3x) \\\Leftrightarrow & -4x-2& = &-1+7-3x \\\Leftrightarrow & -4x \color{red}{-2} & = &6 \color{red}{-3x} \\\Leftrightarrow & -4x \color{red}{-2} \color{blue}{+2} \color{blue}{+3x} & = &6 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+2} \\\Leftrightarrow & -4x+3x& = &6+2 \\\Leftrightarrow & -x& = &8 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{8}{ \color{red}{-1} } \\\Leftrightarrow & x = -8 & & \\ & V = \left\{ -8 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (-4x-5)& = & -15 \color{red}{-} (10+x) \\\Leftrightarrow & -24x-30& = &-15-10-x \\\Leftrightarrow & -24x \color{red}{-30} & = &-25 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{-30} \color{blue}{+30} \color{blue}{+x} & = &-25 \color{red}{-x} \color{blue}{+x} \color{blue}{+30} \\\Leftrightarrow & -24x+x& = &-25+30 \\\Leftrightarrow & -23x& = &5 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{5}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-5}{23} & & \\ & V = \left\{ \frac{-5}{23} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (3x-7)& = & 10 \color{red}{-} (14+x) \\\Leftrightarrow & 12x-28& = &10-14-x \\\Leftrightarrow & 12x \color{red}{-28} & = &-4 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-28} \color{blue}{+28} \color{blue}{+x} & = &-4 \color{red}{-x} \color{blue}{+x} \color{blue}{+28} \\\Leftrightarrow & 12x+x& = &-4+28 \\\Leftrightarrow & 13x& = &24 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{24}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{24}{13} & & \\ & V = \left\{ \frac{24}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (x+4)& = & 4 \color{red}{-} (1-5x) \\\Leftrightarrow & 3x+12& = &4-1+5x \\\Leftrightarrow & 3x \color{red}{+12} & = &3 \color{red}{+5x} \\\Leftrightarrow & 3x \color{red}{+12} \color{blue}{-12} \color{blue}{-5x} & = &3 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-12} \\\Leftrightarrow & 3x-5x& = &3-12 \\\Leftrightarrow & -2x& = &-9 \\\Leftrightarrow & \frac{-2x}{ \color{red}{-2} }& = &\frac{-9}{ \color{red}{-2} } \\\Leftrightarrow & x = \frac{9}{2} & & \\ & V = \left\{ \frac{9}{2} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (-x+3)& = & 15 \color{red}{-} (-13+x) \\\Leftrightarrow & -2x+6& = &15+13-x \\\Leftrightarrow & -2x \color{red}{+6} & = &28 \color{red}{-x} \\\Leftrightarrow & -2x \color{red}{+6} \color{blue}{-6} \color{blue}{+x} & = &28 \color{red}{-x} \color{blue}{+x} \color{blue}{-6} \\\Leftrightarrow & -2x+x& = &28-6 \\\Leftrightarrow & -x& = &22 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{22}{ \color{red}{-1} } \\\Leftrightarrow & x = -22 & & \\ & V = \left\{ -22 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (-3x-5)& = & 5 \color{red}{+} (-9+x) \\\Leftrightarrow & -12x-20& = &5-9+x \\\Leftrightarrow & -12x \color{red}{-20} & = &-4 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-20} \color{blue}{+20} \color{blue}{-x} & = &-4 \color{red}{+x} \color{blue}{-x} \color{blue}{+20} \\\Leftrightarrow & -12x-x& = &-4+20 \\\Leftrightarrow & -13x& = &16 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{16}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-16}{13} & & \\ & V = \left\{ \frac{-16}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (-x+1)& = & 10 \color{red}{-} (-9+x) \\\Leftrightarrow & -4x+4& = &10+9-x \\\Leftrightarrow & -4x \color{red}{+4} & = &19 \color{red}{-x} \\\Leftrightarrow & -4x \color{red}{+4} \color{blue}{-4} \color{blue}{+x} & = &19 \color{red}{-x} \color{blue}{+x} \color{blue}{-4} \\\Leftrightarrow & -4x+x& = &19-4 \\\Leftrightarrow & -3x& = &15 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{15}{ \color{red}{-3} } \\\Leftrightarrow & x = -5 & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (3x+7)& = & 4 \color{red}{+} (6+x) \\\Leftrightarrow & 12x+28& = &4+6+x \\\Leftrightarrow & 12x \color{red}{+28} & = &10 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+28} \color{blue}{-28} \color{blue}{-x} & = &10 \color{red}{+x} \color{blue}{-x} \color{blue}{-28} \\\Leftrightarrow & 12x-x& = &10-28 \\\Leftrightarrow & 11x& = &-18 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-18}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-18}{11} & & \\ & V = \left\{ \frac{-18}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (6x-7)& = & 1 \color{red}{-} (2-5x) \\\Leftrightarrow & 36x-42& = &1-2+5x \\\Leftrightarrow & 36x \color{red}{-42} & = &-1 \color{red}{+5x} \\\Leftrightarrow & 36x \color{red}{-42} \color{blue}{+42} \color{blue}{-5x} & = &-1 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+42} \\\Leftrightarrow & 36x-5x& = &-1+42 \\\Leftrightarrow & 31x& = &41 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{41}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{41}{31} & & \\ & V = \left\{ \frac{41}{31} \right\} & \\\end{align}\)