Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (-4x-5)& = & -1 \color{red}{+} (-4+x) \\\Leftrightarrow & -12x-15& = &-1-4+x \\\Leftrightarrow & -12x \color{red}{-15} & = &-5 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-15} \color{blue}{+15} \color{blue}{-x} & = &-5 \color{red}{+x} \color{blue}{-x} \color{blue}{+15} \\\Leftrightarrow & -12x-x& = &-5+15 \\\Leftrightarrow & -13x& = &10 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{10}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-10}{13} & & \\ & V = \left\{ \frac{-10}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (3x+6)& = & -9 \color{red}{-} (-6+x) \\\Leftrightarrow & 12x+24& = &-9+6-x \\\Leftrightarrow & 12x \color{red}{+24} & = &-3 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+24} \color{blue}{-24} \color{blue}{+x} & = &-3 \color{red}{-x} \color{blue}{+x} \color{blue}{-24} \\\Leftrightarrow & 12x+x& = &-3-24 \\\Leftrightarrow & 13x& = &-27 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-27}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-27}{13} & & \\ & V = \left\{ \frac{-27}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (4x-2)& = & 3 \color{red}{+} (8-5x) \\\Leftrightarrow & 8x-4& = &3+8-5x \\\Leftrightarrow & 8x \color{red}{-4} & = &11 \color{red}{-5x} \\\Leftrightarrow & 8x \color{red}{-4} \color{blue}{+4} \color{blue}{+5x} & = &11 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+4} \\\Leftrightarrow & 8x+5x& = &11+4 \\\Leftrightarrow & 13x& = &15 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{15}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{15}{13} & & \\ & V = \left\{ \frac{15}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (-4x+3)& = & -8 \color{red}{-} (4+x) \\\Leftrightarrow & -12x+9& = &-8-4-x \\\Leftrightarrow & -12x \color{red}{+9} & = &-12 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+9} \color{blue}{-9} \color{blue}{+x} & = &-12 \color{red}{-x} \color{blue}{+x} \color{blue}{-9} \\\Leftrightarrow & -12x+x& = &-12-9 \\\Leftrightarrow & -11x& = &-21 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-21}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{21}{11} & & \\ & V = \left\{ \frac{21}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (-3x-4)& = & 15 \color{red}{+} (-4-2x) \\\Leftrightarrow & -9x-12& = &15-4-2x \\\Leftrightarrow & -9x \color{red}{-12} & = &11 \color{red}{-2x} \\\Leftrightarrow & -9x \color{red}{-12} \color{blue}{+12} \color{blue}{+2x} & = &11 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+12} \\\Leftrightarrow & -9x+2x& = &11+12 \\\Leftrightarrow & -7x& = &23 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{23}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-23}{7} & & \\ & V = \left\{ \frac{-23}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (-6x+5)& = & -15 \color{red}{+} (4-5x) \\\Leftrightarrow & -36x+30& = &-15+4-5x \\\Leftrightarrow & -36x \color{red}{+30} & = &-11 \color{red}{-5x} \\\Leftrightarrow & -36x \color{red}{+30} \color{blue}{-30} \color{blue}{+5x} & = &-11 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-30} \\\Leftrightarrow & -36x+5x& = &-11-30 \\\Leftrightarrow & -31x& = &-41 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{-41}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{41}{31} & & \\ & V = \left\{ \frac{41}{31} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (-3x-4)& = & -6 \color{red}{+} (-10-5x) \\\Leftrightarrow & -18x-24& = &-6-10-5x \\\Leftrightarrow & -18x \color{red}{-24} & = &-16 \color{red}{-5x} \\\Leftrightarrow & -18x \color{red}{-24} \color{blue}{+24} \color{blue}{+5x} & = &-16 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+24} \\\Leftrightarrow & -18x+5x& = &-16+24 \\\Leftrightarrow & -13x& = &8 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{8}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-8}{13} & & \\ & V = \left\{ \frac{-8}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (2x-5)& = & -12 \color{red}{-} (-13+x) \\\Leftrightarrow & 6x-15& = &-12+13-x \\\Leftrightarrow & 6x \color{red}{-15} & = &1 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{-15} \color{blue}{+15} \color{blue}{+x} & = &1 \color{red}{-x} \color{blue}{+x} \color{blue}{+15} \\\Leftrightarrow & 6x+x& = &1+15 \\\Leftrightarrow & 7x& = &16 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{16}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{16}{7} & & \\ & V = \left\{ \frac{16}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (-6x+4)& = & -5 \color{red}{-} (11+x) \\\Leftrightarrow & -12x+8& = &-5-11-x \\\Leftrightarrow & -12x \color{red}{+8} & = &-16 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+8} \color{blue}{-8} \color{blue}{+x} & = &-16 \color{red}{-x} \color{blue}{+x} \color{blue}{-8} \\\Leftrightarrow & -12x+x& = &-16-8 \\\Leftrightarrow & -11x& = &-24 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-24}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{24}{11} & & \\ & V = \left\{ \frac{24}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (-6x-3)& = & 2 \color{red}{-} (-12+x) \\\Leftrightarrow & -24x-12& = &2+12-x \\\Leftrightarrow & -24x \color{red}{-12} & = &14 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &14 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & -24x+x& = &14+12 \\\Leftrightarrow & -23x& = &26 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{26}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-26}{23} & & \\ & V = \left\{ \frac{-26}{23} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (-6x+6)& = & -4 \color{red}{+} (-1+x) \\\Leftrightarrow & -36x+36& = &-4-1+x \\\Leftrightarrow & -36x \color{red}{+36} & = &-5 \color{red}{+x} \\\Leftrightarrow & -36x \color{red}{+36} \color{blue}{-36} \color{blue}{-x} & = &-5 \color{red}{+x} \color{blue}{-x} \color{blue}{-36} \\\Leftrightarrow & -36x-x& = &-5-36 \\\Leftrightarrow & -37x& = &-41 \\\Leftrightarrow & \frac{-37x}{ \color{red}{-37} }& = &\frac{-41}{ \color{red}{-37} } \\\Leftrightarrow & x = \frac{41}{37} & & \\ & V = \left\{ \frac{41}{37} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (4x+1)& = & 5 \color{red}{+} (2+x) \\\Leftrightarrow & 20x+5& = &5+2+x \\\Leftrightarrow & 20x \color{red}{+5} & = &7 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{+5} \color{blue}{-5} \color{blue}{-x} & = &7 \color{red}{+x} \color{blue}{-x} \color{blue}{-5} \\\Leftrightarrow & 20x-x& = &7-5 \\\Leftrightarrow & 19x& = &2 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{2}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{2}{19} & & \\ & V = \left\{ \frac{2}{19} \right\} & \\\end{align}\)