Vgln. eerste graad (reeks 3)

Hoofdmenu Eentje per keer  🖨

Reeks met haakjes

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

---

Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (-3x+4)& = & -2 \color{red}{+} (15+4x) \\\Leftrightarrow & -15x+20& = &-2+15+4x \\\Leftrightarrow & -15x \color{red}{+20} & = &13 \color{red}{+4x} \\\Leftrightarrow & -15x \color{red}{+20} \color{blue}{-20} \color{blue}{-4x} & = &13 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-20} \\\Leftrightarrow & -15x-4x& = &13-20 \\\Leftrightarrow & -19x& = &-7 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-7}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{7}{19} & & \\ & V = \left\{ \frac{7}{19} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (6x+6)& = & -14 \color{red}{+} (-9-5x) \\\Leftrightarrow & 18x+18& = &-14-9-5x \\\Leftrightarrow & 18x \color{red}{+18} & = &-23 \color{red}{-5x} \\\Leftrightarrow & 18x \color{red}{+18} \color{blue}{-18} \color{blue}{+5x} & = &-23 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-18} \\\Leftrightarrow & 18x+5x& = &-23-18 \\\Leftrightarrow & 23x& = &-41 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-41}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-41}{23} & & \\ & V = \left\{ \frac{-41}{23} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (4x-5)& = & -4 \color{red}{+} (-9-3x) \\\Leftrightarrow & 16x-20& = &-4-9-3x \\\Leftrightarrow & 16x \color{red}{-20} & = &-13 \color{red}{-3x} \\\Leftrightarrow & 16x \color{red}{-20} \color{blue}{+20} \color{blue}{+3x} & = &-13 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+20} \\\Leftrightarrow & 16x+3x& = &-13+20 \\\Leftrightarrow & 19x& = &7 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{7}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{7}{19} & & \\ & V = \left\{ \frac{7}{19} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (5x-5)& = & 2 \color{red}{+} (11+x) \\\Leftrightarrow & 30x-30& = &2+11+x \\\Leftrightarrow & 30x \color{red}{-30} & = &13 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{-30} \color{blue}{+30} \color{blue}{-x} & = &13 \color{red}{+x} \color{blue}{-x} \color{blue}{+30} \\\Leftrightarrow & 30x-x& = &13+30 \\\Leftrightarrow & 29x& = &43 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{43}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{43}{29} & & \\ & V = \left\{ \frac{43}{29} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (-6x-4)& = & -5 \color{red}{-} (-12+x) \\\Leftrightarrow & -30x-20& = &-5+12-x \\\Leftrightarrow & -30x \color{red}{-20} & = &7 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{-20} \color{blue}{+20} \color{blue}{+x} & = &7 \color{red}{-x} \color{blue}{+x} \color{blue}{+20} \\\Leftrightarrow & -30x+x& = &7+20 \\\Leftrightarrow & -29x& = &27 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{27}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{-27}{29} & & \\ & V = \left\{ \frac{-27}{29} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (-x-3)& = & -14 \color{red}{-} (7+x) \\\Leftrightarrow & -3x-9& = &-14-7-x \\\Leftrightarrow & -3x \color{red}{-9} & = &-21 \color{red}{-x} \\\Leftrightarrow & -3x \color{red}{-9} \color{blue}{+9} \color{blue}{+x} & = &-21 \color{red}{-x} \color{blue}{+x} \color{blue}{+9} \\\Leftrightarrow & -3x+x& = &-21+9 \\\Leftrightarrow & -2x& = &-12 \\\Leftrightarrow & \frac{-2x}{ \color{red}{-2} }& = &\frac{-12}{ \color{red}{-2} } \\\Leftrightarrow & x = 6 & & \\ & V = \left\{ 6 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (-x-2)& = & 9 \color{red}{+} (2+3x) \\\Leftrightarrow & -4x-8& = &9+2+3x \\\Leftrightarrow & -4x \color{red}{-8} & = &11 \color{red}{+3x} \\\Leftrightarrow & -4x \color{red}{-8} \color{blue}{+8} \color{blue}{-3x} & = &11 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+8} \\\Leftrightarrow & -4x-3x& = &11+8 \\\Leftrightarrow & -7x& = &19 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{19}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-19}{7} & & \\ & V = \left\{ \frac{-19}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (-2x-5)& = & -13 \color{red}{-} (13-5x) \\\Leftrightarrow & -6x-15& = &-13-13+5x \\\Leftrightarrow & -6x \color{red}{-15} & = &-26 \color{red}{+5x} \\\Leftrightarrow & -6x \color{red}{-15} \color{blue}{+15} \color{blue}{-5x} & = &-26 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+15} \\\Leftrightarrow & -6x-5x& = &-26+15 \\\Leftrightarrow & -11x& = &-11 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-11}{ \color{red}{-11} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (-4x-6)& = & 8 \color{red}{-} (15+3x) \\\Leftrightarrow & -20x-30& = &8-15-3x \\\Leftrightarrow & -20x \color{red}{-30} & = &-7 \color{red}{-3x} \\\Leftrightarrow & -20x \color{red}{-30} \color{blue}{+30} \color{blue}{+3x} & = &-7 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+30} \\\Leftrightarrow & -20x+3x& = &-7+30 \\\Leftrightarrow & -17x& = &23 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{23}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{-23}{17} & & \\ & V = \left\{ \frac{-23}{17} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (4x+4)& = & -5 \color{red}{+} (11+x) \\\Leftrightarrow & 20x+20& = &-5+11+x \\\Leftrightarrow & 20x \color{red}{+20} & = &6 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{+20} \color{blue}{-20} \color{blue}{-x} & = &6 \color{red}{+x} \color{blue}{-x} \color{blue}{-20} \\\Leftrightarrow & 20x-x& = &6-20 \\\Leftrightarrow & 19x& = &-14 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-14}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-14}{19} & & \\ & V = \left\{ \frac{-14}{19} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (5x-2)& = & 14 \color{red}{+} (8+3x) \\\Leftrightarrow & 10x-4& = &14+8+3x \\\Leftrightarrow & 10x \color{red}{-4} & = &22 \color{red}{+3x} \\\Leftrightarrow & 10x \color{red}{-4} \color{blue}{+4} \color{blue}{-3x} & = &22 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+4} \\\Leftrightarrow & 10x-3x& = &22+4 \\\Leftrightarrow & 7x& = &26 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{26}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{26}{7} & & \\ & V = \left\{ \frac{26}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (x+5)& = & -8 \color{red}{-} (-2+x) \\\Leftrightarrow & 5x+25& = &-8+2-x \\\Leftrightarrow & 5x \color{red}{+25} & = &-6 \color{red}{-x} \\\Leftrightarrow & 5x \color{red}{+25} \color{blue}{-25} \color{blue}{+x} & = &-6 \color{red}{-x} \color{blue}{+x} \color{blue}{-25} \\\Leftrightarrow & 5x+x& = &-6-25 \\\Leftrightarrow & 6x& = &-31 \\\Leftrightarrow & \frac{6x}{ \color{red}{6} }& = &\frac{-31}{ \color{red}{6} } \\\Leftrightarrow & x = \frac{-31}{6} & & \\ & V = \left\{ \frac{-31}{6} \right\} & \\\end{align}\)