Vgln. eerste graad (reeks 3)

Hoofdmenu Eentje per keer  🖨

Reeks met haakjes

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

---

Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (-2x-6)& = & -6 \color{red}{+} (2-5x) \\\Leftrightarrow & -8x-24& = &-6+2-5x \\\Leftrightarrow & -8x \color{red}{-24} & = &-4 \color{red}{-5x} \\\Leftrightarrow & -8x \color{red}{-24} \color{blue}{+24} \color{blue}{+5x} & = &-4 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+24} \\\Leftrightarrow & -8x+5x& = &-4+24 \\\Leftrightarrow & -3x& = &20 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{20}{ \color{red}{-3} } \\\Leftrightarrow & x = \frac{-20}{3} & & \\ & V = \left\{ \frac{-20}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (-2x+4)& = & 12 \color{red}{+} (3+x) \\\Leftrightarrow & -6x+12& = &12+3+x \\\Leftrightarrow & -6x \color{red}{+12} & = &15 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &15 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & -6x-x& = &15-12 \\\Leftrightarrow & -7x& = &3 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{3}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-3}{7} & & \\ & V = \left\{ \frac{-3}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (3x+5)& = & 8 \color{red}{+} (11+x) \\\Leftrightarrow & 6x+10& = &8+11+x \\\Leftrightarrow & 6x \color{red}{+10} & = &19 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{+10} \color{blue}{-10} \color{blue}{-x} & = &19 \color{red}{+x} \color{blue}{-x} \color{blue}{-10} \\\Leftrightarrow & 6x-x& = &19-10 \\\Leftrightarrow & 5x& = &9 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{9}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{9}{5} & & \\ & V = \left\{ \frac{9}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (-3x+1)& = & 2 \color{red}{+} (15-4x) \\\Leftrightarrow & -9x+3& = &2+15-4x \\\Leftrightarrow & -9x \color{red}{+3} & = &17 \color{red}{-4x} \\\Leftrightarrow & -9x \color{red}{+3} \color{blue}{-3} \color{blue}{+4x} & = &17 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-3} \\\Leftrightarrow & -9x+4x& = &17-3 \\\Leftrightarrow & -5x& = &14 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{14}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-14}{5} & & \\ & V = \left\{ \frac{-14}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (-6x+3)& = & 9 \color{red}{+} (15+x) \\\Leftrightarrow & -24x+12& = &9+15+x \\\Leftrightarrow & -24x \color{red}{+12} & = &24 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &24 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & -24x-x& = &24-12 \\\Leftrightarrow & -25x& = &12 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{12}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{-12}{25} & & \\ & V = \left\{ \frac{-12}{25} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (5x+7)& = & -14 \color{red}{-} (-10+x) \\\Leftrightarrow & 30x+42& = &-14+10-x \\\Leftrightarrow & 30x \color{red}{+42} & = &-4 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{+42} \color{blue}{-42} \color{blue}{+x} & = &-4 \color{red}{-x} \color{blue}{+x} \color{blue}{-42} \\\Leftrightarrow & 30x+x& = &-4-42 \\\Leftrightarrow & 31x& = &-46 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{-46}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{-46}{31} & & \\ & V = \left\{ \frac{-46}{31} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (-3x-3)& = & 13 \color{red}{-} (4+x) \\\Leftrightarrow & -6x-6& = &13-4-x \\\Leftrightarrow & -6x \color{red}{-6} & = &9 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &9 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & -6x+x& = &9+6 \\\Leftrightarrow & -5x& = &15 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{15}{ \color{red}{-5} } \\\Leftrightarrow & x = -3 & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (-2x+7)& = & -9 \color{red}{+} (-9-3x) \\\Leftrightarrow & -10x+35& = &-9-9-3x \\\Leftrightarrow & -10x \color{red}{+35} & = &-18 \color{red}{-3x} \\\Leftrightarrow & -10x \color{red}{+35} \color{blue}{-35} \color{blue}{+3x} & = &-18 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-35} \\\Leftrightarrow & -10x+3x& = &-18-35 \\\Leftrightarrow & -7x& = &-53 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-53}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{53}{7} & & \\ & V = \left\{ \frac{53}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (x-6)& = & 8 \color{red}{-} (-2+x) \\\Leftrightarrow & 6x-36& = &8+2-x \\\Leftrightarrow & 6x \color{red}{-36} & = &10 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{-36} \color{blue}{+36} \color{blue}{+x} & = &10 \color{red}{-x} \color{blue}{+x} \color{blue}{+36} \\\Leftrightarrow & 6x+x& = &10+36 \\\Leftrightarrow & 7x& = &46 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{46}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{46}{7} & & \\ & V = \left\{ \frac{46}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (-3x+5)& = & 4 \color{red}{+} (-7-2x) \\\Leftrightarrow & -15x+25& = &4-7-2x \\\Leftrightarrow & -15x \color{red}{+25} & = &-3 \color{red}{-2x} \\\Leftrightarrow & -15x \color{red}{+25} \color{blue}{-25} \color{blue}{+2x} & = &-3 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-25} \\\Leftrightarrow & -15x+2x& = &-3-25 \\\Leftrightarrow & -13x& = &-28 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-28}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{28}{13} & & \\ & V = \left\{ \frac{28}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (-5x-4)& = & -9 \color{red}{-} (-2+3x) \\\Leftrightarrow & -20x-16& = &-9+2-3x \\\Leftrightarrow & -20x \color{red}{-16} & = &-7 \color{red}{-3x} \\\Leftrightarrow & -20x \color{red}{-16} \color{blue}{+16} \color{blue}{+3x} & = &-7 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+16} \\\Leftrightarrow & -20x+3x& = &-7+16 \\\Leftrightarrow & -17x& = &9 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{9}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{-9}{17} & & \\ & V = \left\{ \frac{-9}{17} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (3x+1)& = & -14 \color{red}{+} (8-4x) \\\Leftrightarrow & 9x+3& = &-14+8-4x \\\Leftrightarrow & 9x \color{red}{+3} & = &-6 \color{red}{-4x} \\\Leftrightarrow & 9x \color{red}{+3} \color{blue}{-3} \color{blue}{+4x} & = &-6 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-3} \\\Leftrightarrow & 9x+4x& = &-6-3 \\\Leftrightarrow & 13x& = &-9 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-9}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-9}{13} & & \\ & V = \left\{ \frac{-9}{13} \right\} & \\\end{align}\)