Vgln. eerste graad (reeks 3)

Hoofdmenu Eentje per keer  🖨

Reeks met haakjes

1. \(4(-2x+4)=5-(11+x)\)
2. \(4(4x-4)=-4-(-3+3x)\)
3. \(3(5x-5)=10-(-7+x)\)
4. \(3(-6x-7)=6-(-11+x)\)
5. \(5(6x-6)=-12+(6+x)\)
6. \(5(-5x-4)=-2+(-15-3x)\)
7. \(4(2x+1)=-10-(-15+3x)\)
8. \(2(6x-1)=-13+(2+5x)\)
9. \(2(-3x-1)=-11+(6+x)\)
10. \(4(4x-1)=5+(14-5x)\)
11. \(6(-5x-7)=-12+(13+29x)\)
12. \(6(x+2)=-5+(11+x)\)

---

Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (-2x+4)& = & 5 \color{red}{-} (11+x) \\\Leftrightarrow & -8x+16& = &5-11-x \\\Leftrightarrow & -8x \color{red}{+16} & = &-6 \color{red}{-x} \\\Leftrightarrow & -8x \color{red}{+16} \color{blue}{-16} \color{blue}{+x} & = &-6 \color{red}{-x} \color{blue}{+x} \color{blue}{-16} \\\Leftrightarrow & -8x+x& = &-6-16 \\\Leftrightarrow & -7x& = &-22 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-22}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{22}{7} & & \\ & V = \left\{ \frac{22}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (4x-4)& = & -4 \color{red}{-} (-3+3x) \\\Leftrightarrow & 16x-16& = &-4+3-3x \\\Leftrightarrow & 16x \color{red}{-16} & = &-1 \color{red}{-3x} \\\Leftrightarrow & 16x \color{red}{-16} \color{blue}{+16} \color{blue}{+3x} & = &-1 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+16} \\\Leftrightarrow & 16x+3x& = &-1+16 \\\Leftrightarrow & 19x& = &15 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{15}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{15}{19} & & \\ & V = \left\{ \frac{15}{19} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (5x-5)& = & 10 \color{red}{-} (-7+x) \\\Leftrightarrow & 15x-15& = &10+7-x \\\Leftrightarrow & 15x \color{red}{-15} & = &17 \color{red}{-x} \\\Leftrightarrow & 15x \color{red}{-15} \color{blue}{+15} \color{blue}{+x} & = &17 \color{red}{-x} \color{blue}{+x} \color{blue}{+15} \\\Leftrightarrow & 15x+x& = &17+15 \\\Leftrightarrow & 16x& = &32 \\\Leftrightarrow & \frac{16x}{ \color{red}{16} }& = &\frac{32}{ \color{red}{16} } \\\Leftrightarrow & x = 2 & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (-6x-7)& = & 6 \color{red}{-} (-11+x) \\\Leftrightarrow & -18x-21& = &6+11-x \\\Leftrightarrow & -18x \color{red}{-21} & = &17 \color{red}{-x} \\\Leftrightarrow & -18x \color{red}{-21} \color{blue}{+21} \color{blue}{+x} & = &17 \color{red}{-x} \color{blue}{+x} \color{blue}{+21} \\\Leftrightarrow & -18x+x& = &17+21 \\\Leftrightarrow & -17x& = &38 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{38}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{-38}{17} & & \\ & V = \left\{ \frac{-38}{17} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (6x-6)& = & -12 \color{red}{+} (6+x) \\\Leftrightarrow & 30x-30& = &-12+6+x \\\Leftrightarrow & 30x \color{red}{-30} & = &-6 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{-30} \color{blue}{+30} \color{blue}{-x} & = &-6 \color{red}{+x} \color{blue}{-x} \color{blue}{+30} \\\Leftrightarrow & 30x-x& = &-6+30 \\\Leftrightarrow & 29x& = &24 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{24}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{24}{29} & & \\ & V = \left\{ \frac{24}{29} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (-5x-4)& = & -2 \color{red}{+} (-15-3x) \\\Leftrightarrow & -25x-20& = &-2-15-3x \\\Leftrightarrow & -25x \color{red}{-20} & = &-17 \color{red}{-3x} \\\Leftrightarrow & -25x \color{red}{-20} \color{blue}{+20} \color{blue}{+3x} & = &-17 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+20} \\\Leftrightarrow & -25x+3x& = &-17+20 \\\Leftrightarrow & -22x& = &3 \\\Leftrightarrow & \frac{-22x}{ \color{red}{-22} }& = &\frac{3}{ \color{red}{-22} } \\\Leftrightarrow & x = \frac{-3}{22} & & \\ & V = \left\{ \frac{-3}{22} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (2x+1)& = & -10 \color{red}{-} (-15+3x) \\\Leftrightarrow & 8x+4& = &-10+15-3x \\\Leftrightarrow & 8x \color{red}{+4} & = &5 \color{red}{-3x} \\\Leftrightarrow & 8x \color{red}{+4} \color{blue}{-4} \color{blue}{+3x} & = &5 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-4} \\\Leftrightarrow & 8x+3x& = &5-4 \\\Leftrightarrow & 11x& = &1 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{1}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{1}{11} & & \\ & V = \left\{ \frac{1}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (6x-1)& = & -13 \color{red}{+} (2+5x) \\\Leftrightarrow & 12x-2& = &-13+2+5x \\\Leftrightarrow & 12x \color{red}{-2} & = &-11 \color{red}{+5x} \\\Leftrightarrow & 12x \color{red}{-2} \color{blue}{+2} \color{blue}{-5x} & = &-11 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+2} \\\Leftrightarrow & 12x-5x& = &-11+2 \\\Leftrightarrow & 7x& = &-9 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-9}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-9}{7} & & \\ & V = \left\{ \frac{-9}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (-3x-1)& = & -11 \color{red}{+} (6+x) \\\Leftrightarrow & -6x-2& = &-11+6+x \\\Leftrightarrow & -6x \color{red}{-2} & = &-5 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{-2} \color{blue}{+2} \color{blue}{-x} & = &-5 \color{red}{+x} \color{blue}{-x} \color{blue}{+2} \\\Leftrightarrow & -6x-x& = &-5+2 \\\Leftrightarrow & -7x& = &-3 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-3}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{3}{7} & & \\ & V = \left\{ \frac{3}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (4x-1)& = & 5 \color{red}{+} (14-5x) \\\Leftrightarrow & 16x-4& = &5+14-5x \\\Leftrightarrow & 16x \color{red}{-4} & = &19 \color{red}{-5x} \\\Leftrightarrow & 16x \color{red}{-4} \color{blue}{+4} \color{blue}{+5x} & = &19 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+4} \\\Leftrightarrow & 16x+5x& = &19+4 \\\Leftrightarrow & 21x& = &23 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{23}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{23}{21} & & \\ & V = \left\{ \frac{23}{21} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (-5x-7)& = & -12 \color{red}{+} (13+29x) \\\Leftrightarrow & -30x-42& = &-12+13+29x \\\Leftrightarrow & -30x \color{red}{-42} & = &1 \color{red}{+29x} \\\Leftrightarrow & -30x \color{red}{-42} \color{blue}{+42} \color{blue}{-29x} & = &1 \color{red}{+29x} \color{blue}{-29x} \color{blue}{+42} \\\Leftrightarrow & -30x-29x& = &1+42 \\\Leftrightarrow & -59x& = &43 \\\Leftrightarrow & \frac{-59x}{ \color{red}{-59} }& = &\frac{43}{ \color{red}{-59} } \\\Leftrightarrow & x = \frac{-43}{59} & & \\ & V = \left\{ \frac{-43}{59} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (x+2)& = & -5 \color{red}{+} (11+x) \\\Leftrightarrow & 6x+12& = &-5+11+x \\\Leftrightarrow & 6x \color{red}{+12} & = &6 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &6 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & 6x-x& = &6-12 \\\Leftrightarrow & 5x& = &-6 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-6}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{-6}{5} & & \\ & V = \left\{ \frac{-6}{5} \right\} & \\\end{align}\)