Vgln. eerste graad (reeks 3)

Hoofdmenu Eentje per keer  🖨

Reeks met haakjes

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

---

Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (-6x+7)& = & 8 \color{red}{+} (-13+x) \\\Leftrightarrow & -30x+35& = &8-13+x \\\Leftrightarrow & -30x \color{red}{+35} & = &-5 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{+35} \color{blue}{-35} \color{blue}{-x} & = &-5 \color{red}{+x} \color{blue}{-x} \color{blue}{-35} \\\Leftrightarrow & -30x-x& = &-5-35 \\\Leftrightarrow & -31x& = &-40 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{-40}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{40}{31} & & \\ & V = \left\{ \frac{40}{31} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (-3x-3)& = & 9 \color{red}{+} (8+x) \\\Leftrightarrow & -9x-9& = &9+8+x \\\Leftrightarrow & -9x \color{red}{-9} & = &17 \color{red}{+x} \\\Leftrightarrow & -9x \color{red}{-9} \color{blue}{+9} \color{blue}{-x} & = &17 \color{red}{+x} \color{blue}{-x} \color{blue}{+9} \\\Leftrightarrow & -9x-x& = &17+9 \\\Leftrightarrow & -10x& = &26 \\\Leftrightarrow & \frac{-10x}{ \color{red}{-10} }& = &\frac{26}{ \color{red}{-10} } \\\Leftrightarrow & x = \frac{-13}{5} & & \\ & V = \left\{ \frac{-13}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (x+3)& = & -5 \color{red}{-} (8+x) \\\Leftrightarrow & 3x+9& = &-5-8-x \\\Leftrightarrow & 3x \color{red}{+9} & = &-13 \color{red}{-x} \\\Leftrightarrow & 3x \color{red}{+9} \color{blue}{-9} \color{blue}{+x} & = &-13 \color{red}{-x} \color{blue}{+x} \color{blue}{-9} \\\Leftrightarrow & 3x+x& = &-13-9 \\\Leftrightarrow & 4x& = &-22 \\\Leftrightarrow & \frac{4x}{ \color{red}{4} }& = &\frac{-22}{ \color{red}{4} } \\\Leftrightarrow & x = \frac{-11}{2} & & \\ & V = \left\{ \frac{-11}{2} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (2x-1)& = & 3 \color{red}{+} (5+x) \\\Leftrightarrow & 6x-3& = &3+5+x \\\Leftrightarrow & 6x \color{red}{-3} & = &8 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{-3} \color{blue}{+3} \color{blue}{-x} & = &8 \color{red}{+x} \color{blue}{-x} \color{blue}{+3} \\\Leftrightarrow & 6x-x& = &8+3 \\\Leftrightarrow & 5x& = &11 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{11}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{11}{5} & & \\ & V = \left\{ \frac{11}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (6x-4)& = & -7 \color{red}{-} (-9+x) \\\Leftrightarrow & 18x-12& = &-7+9-x \\\Leftrightarrow & 18x \color{red}{-12} & = &2 \color{red}{-x} \\\Leftrightarrow & 18x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &2 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & 18x+x& = &2+12 \\\Leftrightarrow & 19x& = &14 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{14}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{14}{19} & & \\ & V = \left\{ \frac{14}{19} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (-6x-3)& = & -3 \color{red}{+} (4+x) \\\Leftrightarrow & -12x-6& = &-3+4+x \\\Leftrightarrow & -12x \color{red}{-6} & = &1 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &1 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & -12x-x& = &1+6 \\\Leftrightarrow & -13x& = &7 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{7}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-7}{13} & & \\ & V = \left\{ \frac{-7}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (6x+7)& = & -13 \color{red}{+} (15+x) \\\Leftrightarrow & 36x+42& = &-13+15+x \\\Leftrightarrow & 36x \color{red}{+42} & = &2 \color{red}{+x} \\\Leftrightarrow & 36x \color{red}{+42} \color{blue}{-42} \color{blue}{-x} & = &2 \color{red}{+x} \color{blue}{-x} \color{blue}{-42} \\\Leftrightarrow & 36x-x& = &2-42 \\\Leftrightarrow & 35x& = &-40 \\\Leftrightarrow & \frac{35x}{ \color{red}{35} }& = &\frac{-40}{ \color{red}{35} } \\\Leftrightarrow & x = \frac{-8}{7} & & \\ & V = \left\{ \frac{-8}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (-4x-1)& = & -6 \color{red}{+} (14+x) \\\Leftrightarrow & -8x-2& = &-6+14+x \\\Leftrightarrow & -8x \color{red}{-2} & = &8 \color{red}{+x} \\\Leftrightarrow & -8x \color{red}{-2} \color{blue}{+2} \color{blue}{-x} & = &8 \color{red}{+x} \color{blue}{-x} \color{blue}{+2} \\\Leftrightarrow & -8x-x& = &8+2 \\\Leftrightarrow & -9x& = &10 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{10}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{-10}{9} & & \\ & V = \left\{ \frac{-10}{9} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (5x+6)& = & -15 \color{red}{+} (-4+3x) \\\Leftrightarrow & 20x+24& = &-15-4+3x \\\Leftrightarrow & 20x \color{red}{+24} & = &-19 \color{red}{+3x} \\\Leftrightarrow & 20x \color{red}{+24} \color{blue}{-24} \color{blue}{-3x} & = &-19 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-24} \\\Leftrightarrow & 20x-3x& = &-19-24 \\\Leftrightarrow & 17x& = &-43 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{-43}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{-43}{17} & & \\ & V = \left\{ \frac{-43}{17} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (-3x-6)& = & 3 \color{red}{+} (-15-5x) \\\Leftrightarrow & -18x-36& = &3-15-5x \\\Leftrightarrow & -18x \color{red}{-36} & = &-12 \color{red}{-5x} \\\Leftrightarrow & -18x \color{red}{-36} \color{blue}{+36} \color{blue}{+5x} & = &-12 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+36} \\\Leftrightarrow & -18x+5x& = &-12+36 \\\Leftrightarrow & -13x& = &24 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{24}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-24}{13} & & \\ & V = \left\{ \frac{-24}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (-4x+5)& = & -4 \color{red}{-} (1+x) \\\Leftrightarrow & -24x+30& = &-4-1-x \\\Leftrightarrow & -24x \color{red}{+30} & = &-5 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{+30} \color{blue}{-30} \color{blue}{+x} & = &-5 \color{red}{-x} \color{blue}{+x} \color{blue}{-30} \\\Leftrightarrow & -24x+x& = &-5-30 \\\Leftrightarrow & -23x& = &-35 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-35}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{35}{23} & & \\ & V = \left\{ \frac{35}{23} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (2x-6)& = & 4 \color{red}{+} (9+x) \\\Leftrightarrow & 12x-36& = &4+9+x \\\Leftrightarrow & 12x \color{red}{-36} & = &13 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-36} \color{blue}{+36} \color{blue}{-x} & = &13 \color{red}{+x} \color{blue}{-x} \color{blue}{+36} \\\Leftrightarrow & 12x-x& = &13+36 \\\Leftrightarrow & 11x& = &49 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{49}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{49}{11} & & \\ & V = \left\{ \frac{49}{11} \right\} & \\\end{align}\)