Vgln. eerste graad (reeks 3)

reeks met haakjes

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

reeks met haakjes

Verbetersleutel

1. \begin{align} & \color{red}{3} (x+4)& = & 2 \color{red}{+} (-5+4x) \\\Leftrightarrow & 3x+12& = &2-5+4x \\\Leftrightarrow & 3x \color{red}{+12} & = &-3 \color{red}{+4x} \\\Leftrightarrow & 3x \color{red}{+12} \color{blue}{-12} \color{blue}{-4x} & = &-3 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-12} \\\Leftrightarrow & 3x-4x& = &-3-12 \\\Leftrightarrow & -x& = &-15 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-15}{ \color{red}{-1} } \\\Leftrightarrow & x = 15 & & \\\end{align}
2. \begin{align} & \color{red}{2} (4x+3)& = & -2 \color{red}{+} (8-5x) \\\Leftrightarrow & 8x+6& = &-2+8-5x \\\Leftrightarrow & 8x \color{red}{+6} & = &6 \color{red}{-5x} \\\Leftrightarrow & 8x \color{red}{+6} \color{blue}{-6} \color{blue}{+5x} & = &6 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-6} \\\Leftrightarrow & 8x+5x& = &6-6 \\\Leftrightarrow & 13x& = &0 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{0}{ \color{red}{13} } \\\Leftrightarrow & x = 0 & & \\\end{align}
3. \begin{align} & \color{red}{4} (-x-7)& = & -3 \color{red}{+} (-12+3x) \\\Leftrightarrow & -4x-28& = &-3-12+3x \\\Leftrightarrow & -4x \color{red}{-28} & = &-15 \color{red}{+3x} \\\Leftrightarrow & -4x \color{red}{-28} \color{blue}{+28} \color{blue}{-3x} & = &-15 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+28} \\\Leftrightarrow & -4x-3x& = &-15+28 \\\Leftrightarrow & -7x& = &13 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{13}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-13}{7} & & \\\end{align}
4. \begin{align} & \color{red}{6} (5x+3)& = & 14 \color{red}{+} (-1+x) \\\Leftrightarrow & 30x+18& = &14-1+x \\\Leftrightarrow & 30x \color{red}{+18} & = &13 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{+18} \color{blue}{-18} \color{blue}{-x} & = &13 \color{red}{+x} \color{blue}{-x} \color{blue}{-18} \\\Leftrightarrow & 30x-x& = &13-18 \\\Leftrightarrow & 29x& = &-5 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{-5}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{-5}{29} & & \\\end{align}
5. \begin{align} & \color{red}{3} (x-5)& = & 7 \color{red}{+} (10-2x) \\\Leftrightarrow & 3x-15& = &7+10-2x \\\Leftrightarrow & 3x \color{red}{-15} & = &17 \color{red}{-2x} \\\Leftrightarrow & 3x \color{red}{-15} \color{blue}{+15} \color{blue}{+2x} & = &17 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+15} \\\Leftrightarrow & 3x+2x& = &17+15 \\\Leftrightarrow & 5x& = &32 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{32}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{32}{5} & & \\\end{align}
6. \begin{align} & \color{red}{2} (3x+1)& = & -10 \color{red}{-} (-9-5x) \\\Leftrightarrow & 6x+2& = &-10+9+5x \\\Leftrightarrow & 6x \color{red}{+2} & = &-1 \color{red}{+5x} \\\Leftrightarrow & 6x \color{red}{+2} \color{blue}{-2} \color{blue}{-5x} & = &-1 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-2} \\\Leftrightarrow & 6x-5x& = &-1-2 \\\Leftrightarrow & x& = &-3 \\\end{align}
7. \begin{align} & \color{red}{6} (5x-6)& = & 11 \color{red}{-} (10+x) \\\Leftrightarrow & 30x-36& = &11-10-x \\\Leftrightarrow & 30x \color{red}{-36} & = &1 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{-36} \color{blue}{+36} \color{blue}{+x} & = &1 \color{red}{-x} \color{blue}{+x} \color{blue}{+36} \\\Leftrightarrow & 30x+x& = &1+36 \\\Leftrightarrow & 31x& = &37 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{37}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{37}{31} & & \\\end{align}
8. \begin{align} & \color{red}{6} (-x-6)& = & 13 \color{red}{-} (1+5x) \\\Leftrightarrow & -6x-36& = &13-1-5x \\\Leftrightarrow & -6x \color{red}{-36} & = &12 \color{red}{-5x} \\\Leftrightarrow & -6x \color{red}{-36} \color{blue}{+36} \color{blue}{+5x} & = &12 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+36} \\\Leftrightarrow & -6x+5x& = &12+36 \\\Leftrightarrow & -x& = &48 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{48}{ \color{red}{-1} } \\\Leftrightarrow & x = -48 & & \\\end{align}
9. \begin{align} & \color{red}{3} (-2x-3)& = & -12 \color{red}{-} (9+5x) \\\Leftrightarrow & -6x-9& = &-12-9-5x \\\Leftrightarrow & -6x \color{red}{-9} & = &-21 \color{red}{-5x} \\\Leftrightarrow & -6x \color{red}{-9} \color{blue}{+9} \color{blue}{+5x} & = &-21 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+9} \\\Leftrightarrow & -6x+5x& = &-21+9 \\\Leftrightarrow & -x& = &-12 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-12}{ \color{red}{-1} } \\\Leftrightarrow & x = 12 & & \\\end{align}
10. \begin{align} & \color{red}{6} (-4x-2)& = & 3 \color{red}{-} (13+x) \\\Leftrightarrow & -24x-12& = &3-13-x \\\Leftrightarrow & -24x \color{red}{-12} & = &-10 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &-10 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & -24x+x& = &-10+12 \\\Leftrightarrow & -23x& = &2 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{2}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-2}{23} & & \\\end{align}
11. \begin{align} & \color{red}{5} (2x+7)& = & -15 \color{red}{-} (-2+x) \\\Leftrightarrow & 10x+35& = &-15+2-x \\\Leftrightarrow & 10x \color{red}{+35} & = &-13 \color{red}{-x} \\\Leftrightarrow & 10x \color{red}{+35} \color{blue}{-35} \color{blue}{+x} & = &-13 \color{red}{-x} \color{blue}{+x} \color{blue}{-35} \\\Leftrightarrow & 10x+x& = &-13-35 \\\Leftrightarrow & 11x& = &-48 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-48}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-48}{11} & & \\\end{align}
12. \begin{align} & \color{red}{5} (2x-4)& = & 12 \color{red}{+} (15-3x) \\\Leftrightarrow & 10x-20& = &12+15-3x \\\Leftrightarrow & 10x \color{red}{-20} & = &27 \color{red}{-3x} \\\Leftrightarrow & 10x \color{red}{-20} \color{blue}{+20} \color{blue}{+3x} & = &27 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+20} \\\Leftrightarrow & 10x+3x& = &27+20 \\\Leftrightarrow & 13x& = &47 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{47}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{47}{13} & & \\\end{align}
Oefeningengenerator vanhoeckes.be/wiskunde 2022-06-27 08:21:48