Vgln. eerste graad (reeks 3)

Hoofdmenu Eentje per keer  🖨

Reeks met haakjes

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

---

Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (-x+5)& = & 10 \color{red}{-} (6+x) \\\Leftrightarrow & -2x+10& = &10-6-x \\\Leftrightarrow & -2x \color{red}{+10} & = &4 \color{red}{-x} \\\Leftrightarrow & -2x \color{red}{+10} \color{blue}{-10} \color{blue}{+x} & = &4 \color{red}{-x} \color{blue}{+x} \color{blue}{-10} \\\Leftrightarrow & -2x+x& = &4-10 \\\Leftrightarrow & -x& = &-6 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-6}{ \color{red}{-1} } \\\Leftrightarrow & x = 6 & & \\ & V = \left\{ 6 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (-4x+1)& = & -14 \color{red}{-} (7+x) \\\Leftrightarrow & -8x+2& = &-14-7-x \\\Leftrightarrow & -8x \color{red}{+2} & = &-21 \color{red}{-x} \\\Leftrightarrow & -8x \color{red}{+2} \color{blue}{-2} \color{blue}{+x} & = &-21 \color{red}{-x} \color{blue}{+x} \color{blue}{-2} \\\Leftrightarrow & -8x+x& = &-21-2 \\\Leftrightarrow & -7x& = &-23 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-23}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{23}{7} & & \\ & V = \left\{ \frac{23}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (-2x-5)& = & -15 \color{red}{+} (-4+x) \\\Leftrightarrow & -6x-15& = &-15-4+x \\\Leftrightarrow & -6x \color{red}{-15} & = &-19 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{-15} \color{blue}{+15} \color{blue}{-x} & = &-19 \color{red}{+x} \color{blue}{-x} \color{blue}{+15} \\\Leftrightarrow & -6x-x& = &-19+15 \\\Leftrightarrow & -7x& = &-4 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-4}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{4}{7} & & \\ & V = \left\{ \frac{4}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (2x-1)& = & -9 \color{red}{-} (5+x) \\\Leftrightarrow & 6x-3& = &-9-5-x \\\Leftrightarrow & 6x \color{red}{-3} & = &-14 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{-3} \color{blue}{+3} \color{blue}{+x} & = &-14 \color{red}{-x} \color{blue}{+x} \color{blue}{+3} \\\Leftrightarrow & 6x+x& = &-14+3 \\\Leftrightarrow & 7x& = &-11 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-11}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-11}{7} & & \\ & V = \left\{ \frac{-11}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (-2x-2)& = & -1 \color{red}{+} (12+x) \\\Leftrightarrow & -8x-8& = &-1+12+x \\\Leftrightarrow & -8x \color{red}{-8} & = &11 \color{red}{+x} \\\Leftrightarrow & -8x \color{red}{-8} \color{blue}{+8} \color{blue}{-x} & = &11 \color{red}{+x} \color{blue}{-x} \color{blue}{+8} \\\Leftrightarrow & -8x-x& = &11+8 \\\Leftrightarrow & -9x& = &19 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{19}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{-19}{9} & & \\ & V = \left\{ \frac{-19}{9} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (-4x+1)& = & -6 \color{red}{+} (13+x) \\\Leftrightarrow & -12x+3& = &-6+13+x \\\Leftrightarrow & -12x \color{red}{+3} & = &7 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+3} \color{blue}{-3} \color{blue}{-x} & = &7 \color{red}{+x} \color{blue}{-x} \color{blue}{-3} \\\Leftrightarrow & -12x-x& = &7-3 \\\Leftrightarrow & -13x& = &4 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{4}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-4}{13} & & \\ & V = \left\{ \frac{-4}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (-6x+2)& = & -5 \color{red}{+} (9+x) \\\Leftrightarrow & -24x+8& = &-5+9+x \\\Leftrightarrow & -24x \color{red}{+8} & = &4 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{+8} \color{blue}{-8} \color{blue}{-x} & = &4 \color{red}{+x} \color{blue}{-x} \color{blue}{-8} \\\Leftrightarrow & -24x-x& = &4-8 \\\Leftrightarrow & -25x& = &-4 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{-4}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{4}{25} & & \\ & V = \left\{ \frac{4}{25} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (x-7)& = & 8 \color{red}{-} (11-4x) \\\Leftrightarrow & 5x-35& = &8-11+4x \\\Leftrightarrow & 5x \color{red}{-35} & = &-3 \color{red}{+4x} \\\Leftrightarrow & 5x \color{red}{-35} \color{blue}{+35} \color{blue}{-4x} & = &-3 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+35} \\\Leftrightarrow & 5x-4x& = &-3+35 \\\Leftrightarrow & x& = &32 \\ & V = \left\{ 32 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (-5x-1)& = & -15 \color{red}{-} (14+2x) \\\Leftrightarrow & -25x-5& = &-15-14-2x \\\Leftrightarrow & -25x \color{red}{-5} & = &-29 \color{red}{-2x} \\\Leftrightarrow & -25x \color{red}{-5} \color{blue}{+5} \color{blue}{+2x} & = &-29 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+5} \\\Leftrightarrow & -25x+2x& = &-29+5 \\\Leftrightarrow & -23x& = &-24 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-24}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{24}{23} & & \\ & V = \left\{ \frac{24}{23} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (-5x+2)& = & 3 \color{red}{+} (10+x) \\\Leftrightarrow & -25x+10& = &3+10+x \\\Leftrightarrow & -25x \color{red}{+10} & = &13 \color{red}{+x} \\\Leftrightarrow & -25x \color{red}{+10} \color{blue}{-10} \color{blue}{-x} & = &13 \color{red}{+x} \color{blue}{-x} \color{blue}{-10} \\\Leftrightarrow & -25x-x& = &13-10 \\\Leftrightarrow & -26x& = &3 \\\Leftrightarrow & \frac{-26x}{ \color{red}{-26} }& = &\frac{3}{ \color{red}{-26} } \\\Leftrightarrow & x = \frac{-3}{26} & & \\ & V = \left\{ \frac{-3}{26} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (6x+2)& = & -2 \color{red}{+} (-13+x) \\\Leftrightarrow & 18x+6& = &-2-13+x \\\Leftrightarrow & 18x \color{red}{+6} & = &-15 \color{red}{+x} \\\Leftrightarrow & 18x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &-15 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & 18x-x& = &-15-6 \\\Leftrightarrow & 17x& = &-21 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{-21}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{-21}{17} & & \\ & V = \left\{ \frac{-21}{17} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (-2x+7)& = & 6 \color{red}{-} (8+x) \\\Leftrightarrow & -10x+35& = &6-8-x \\\Leftrightarrow & -10x \color{red}{+35} & = &-2 \color{red}{-x} \\\Leftrightarrow & -10x \color{red}{+35} \color{blue}{-35} \color{blue}{+x} & = &-2 \color{red}{-x} \color{blue}{+x} \color{blue}{-35} \\\Leftrightarrow & -10x+x& = &-2-35 \\\Leftrightarrow & -9x& = &-37 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{-37}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{37}{9} & & \\ & V = \left\{ \frac{37}{9} \right\} & \\\end{align}\)