Vgln. eerste graad (reeks 3)

Hoofdmenu Eentje per keer  🖨

Reeks met haakjes

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

---

Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (-3x+6)& = & 1 \color{red}{-} (12-5x) \\\Leftrightarrow & -18x+36& = &1-12+5x \\\Leftrightarrow & -18x \color{red}{+36} & = &-11 \color{red}{+5x} \\\Leftrightarrow & -18x \color{red}{+36} \color{blue}{-36} \color{blue}{-5x} & = &-11 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-36} \\\Leftrightarrow & -18x-5x& = &-11-36 \\\Leftrightarrow & -23x& = &-47 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-47}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{47}{23} & & \\ & V = \left\{ \frac{47}{23} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (-6x-2)& = & 1 \color{red}{-} (-9+x) \\\Leftrightarrow & -36x-12& = &1+9-x \\\Leftrightarrow & -36x \color{red}{-12} & = &10 \color{red}{-x} \\\Leftrightarrow & -36x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &10 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & -36x+x& = &10+12 \\\Leftrightarrow & -35x& = &22 \\\Leftrightarrow & \frac{-35x}{ \color{red}{-35} }& = &\frac{22}{ \color{red}{-35} } \\\Leftrightarrow & x = \frac{-22}{35} & & \\ & V = \left\{ \frac{-22}{35} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (-6x-3)& = & 15 \color{red}{-} (8+x) \\\Leftrightarrow & -36x-18& = &15-8-x \\\Leftrightarrow & -36x \color{red}{-18} & = &7 \color{red}{-x} \\\Leftrightarrow & -36x \color{red}{-18} \color{blue}{+18} \color{blue}{+x} & = &7 \color{red}{-x} \color{blue}{+x} \color{blue}{+18} \\\Leftrightarrow & -36x+x& = &7+18 \\\Leftrightarrow & -35x& = &25 \\\Leftrightarrow & \frac{-35x}{ \color{red}{-35} }& = &\frac{25}{ \color{red}{-35} } \\\Leftrightarrow & x = \frac{-5}{7} & & \\ & V = \left\{ \frac{-5}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (3x+2)& = & -3 \color{red}{-} (-11-2x) \\\Leftrightarrow & 9x+6& = &-3+11+2x \\\Leftrightarrow & 9x \color{red}{+6} & = &8 \color{red}{+2x} \\\Leftrightarrow & 9x \color{red}{+6} \color{blue}{-6} \color{blue}{-2x} & = &8 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-6} \\\Leftrightarrow & 9x-2x& = &8-6 \\\Leftrightarrow & 7x& = &2 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{2}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{2}{7} & & \\ & V = \left\{ \frac{2}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (2x+5)& = & 11 \color{red}{+} (14-3x) \\\Leftrightarrow & 10x+25& = &11+14-3x \\\Leftrightarrow & 10x \color{red}{+25} & = &25 \color{red}{-3x} \\\Leftrightarrow & 10x \color{red}{+25} \color{blue}{-25} \color{blue}{+3x} & = &25 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-25} \\\Leftrightarrow & 10x+3x& = &25-25 \\\Leftrightarrow & 13x& = &0 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{0}{ \color{red}{13} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (x-7)& = & -2 \color{red}{-} (9+x) \\\Leftrightarrow & 6x-42& = &-2-9-x \\\Leftrightarrow & 6x \color{red}{-42} & = &-11 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{-42} \color{blue}{+42} \color{blue}{+x} & = &-11 \color{red}{-x} \color{blue}{+x} \color{blue}{+42} \\\Leftrightarrow & 6x+x& = &-11+42 \\\Leftrightarrow & 7x& = &31 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{31}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{31}{7} & & \\ & V = \left\{ \frac{31}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (-x+6)& = & 11 \color{red}{+} (-12+4x) \\\Leftrightarrow & -3x+18& = &11-12+4x \\\Leftrightarrow & -3x \color{red}{+18} & = &-1 \color{red}{+4x} \\\Leftrightarrow & -3x \color{red}{+18} \color{blue}{-18} \color{blue}{-4x} & = &-1 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-18} \\\Leftrightarrow & -3x-4x& = &-1-18 \\\Leftrightarrow & -7x& = &-19 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-19}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{19}{7} & & \\ & V = \left\{ \frac{19}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (-3x-7)& = & 4 \color{red}{+} (-8+x) \\\Leftrightarrow & -6x-14& = &4-8+x \\\Leftrightarrow & -6x \color{red}{-14} & = &-4 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{-14} \color{blue}{+14} \color{blue}{-x} & = &-4 \color{red}{+x} \color{blue}{-x} \color{blue}{+14} \\\Leftrightarrow & -6x-x& = &-4+14 \\\Leftrightarrow & -7x& = &10 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{10}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-10}{7} & & \\ & V = \left\{ \frac{-10}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (4x-7)& = & -1 \color{red}{-} (-3+x) \\\Leftrightarrow & 16x-28& = &-1+3-x \\\Leftrightarrow & 16x \color{red}{-28} & = &2 \color{red}{-x} \\\Leftrightarrow & 16x \color{red}{-28} \color{blue}{+28} \color{blue}{+x} & = &2 \color{red}{-x} \color{blue}{+x} \color{blue}{+28} \\\Leftrightarrow & 16x+x& = &2+28 \\\Leftrightarrow & 17x& = &30 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{30}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{30}{17} & & \\ & V = \left\{ \frac{30}{17} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (-3x-7)& = & 9 \color{red}{-} (-4-5x) \\\Leftrightarrow & -18x-42& = &9+4+5x \\\Leftrightarrow & -18x \color{red}{-42} & = &13 \color{red}{+5x} \\\Leftrightarrow & -18x \color{red}{-42} \color{blue}{+42} \color{blue}{-5x} & = &13 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+42} \\\Leftrightarrow & -18x-5x& = &13+42 \\\Leftrightarrow & -23x& = &55 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{55}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-55}{23} & & \\ & V = \left\{ \frac{-55}{23} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (5x+6)& = & -10 \color{red}{-} (-11+x) \\\Leftrightarrow & 25x+30& = &-10+11-x \\\Leftrightarrow & 25x \color{red}{+30} & = &1 \color{red}{-x} \\\Leftrightarrow & 25x \color{red}{+30} \color{blue}{-30} \color{blue}{+x} & = &1 \color{red}{-x} \color{blue}{+x} \color{blue}{-30} \\\Leftrightarrow & 25x+x& = &1-30 \\\Leftrightarrow & 26x& = &-29 \\\Leftrightarrow & \frac{26x}{ \color{red}{26} }& = &\frac{-29}{ \color{red}{26} } \\\Leftrightarrow & x = \frac{-29}{26} & & \\ & V = \left\{ \frac{-29}{26} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (4x-1)& = & 2 \color{red}{+} (-13+x) \\\Leftrightarrow & 8x-2& = &2-13+x \\\Leftrightarrow & 8x \color{red}{-2} & = &-11 \color{red}{+x} \\\Leftrightarrow & 8x \color{red}{-2} \color{blue}{+2} \color{blue}{-x} & = &-11 \color{red}{+x} \color{blue}{-x} \color{blue}{+2} \\\Leftrightarrow & 8x-x& = &-11+2 \\\Leftrightarrow & 7x& = &-9 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-9}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-9}{7} & & \\ & V = \left\{ \frac{-9}{7} \right\} & \\\end{align}\)