Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (-2x+3)& = & -6 \color{red}{+} (4+x) \\\Leftrightarrow & -8x+12& = &-6+4+x \\\Leftrightarrow & -8x \color{red}{+12} & = &-2 \color{red}{+x} \\\Leftrightarrow & -8x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &-2 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & -8x-x& = &-2-12 \\\Leftrightarrow & -9x& = &-14 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{-14}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{14}{9} & & \\ & V = \left\{ \frac{14}{9} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (4x-2)& = & -10 \color{red}{+} (-3+3x) \\\Leftrightarrow & 8x-4& = &-10-3+3x \\\Leftrightarrow & 8x \color{red}{-4} & = &-13 \color{red}{+3x} \\\Leftrightarrow & 8x \color{red}{-4} \color{blue}{+4} \color{blue}{-3x} & = &-13 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+4} \\\Leftrightarrow & 8x-3x& = &-13+4 \\\Leftrightarrow & 5x& = &-9 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-9}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{-9}{5} & & \\ & V = \left\{ \frac{-9}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (-2x-1)& = & -9 \color{red}{-} (-6-5x) \\\Leftrightarrow & -6x-3& = &-9+6+5x \\\Leftrightarrow & -6x \color{red}{-3} & = &-3 \color{red}{+5x} \\\Leftrightarrow & -6x \color{red}{-3} \color{blue}{+3} \color{blue}{-5x} & = &-3 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+3} \\\Leftrightarrow & -6x-5x& = &-3+3 \\\Leftrightarrow & -11x& = &0 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{0}{ \color{red}{-11} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (-3x+6)& = & -9 \color{red}{+} (-10+x) \\\Leftrightarrow & -18x+36& = &-9-10+x \\\Leftrightarrow & -18x \color{red}{+36} & = &-19 \color{red}{+x} \\\Leftrightarrow & -18x \color{red}{+36} \color{blue}{-36} \color{blue}{-x} & = &-19 \color{red}{+x} \color{blue}{-x} \color{blue}{-36} \\\Leftrightarrow & -18x-x& = &-19-36 \\\Leftrightarrow & -19x& = &-55 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-55}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{55}{19} & & \\ & V = \left\{ \frac{55}{19} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (4x+7)& = & 5 \color{red}{+} (-13+x) \\\Leftrightarrow & 24x+42& = &5-13+x \\\Leftrightarrow & 24x \color{red}{+42} & = &-8 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{+42} \color{blue}{-42} \color{blue}{-x} & = &-8 \color{red}{+x} \color{blue}{-x} \color{blue}{-42} \\\Leftrightarrow & 24x-x& = &-8-42 \\\Leftrightarrow & 23x& = &-50 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-50}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-50}{23} & & \\ & V = \left\{ \frac{-50}{23} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (4x-4)& = & 14 \color{red}{-} (6+x) \\\Leftrightarrow & 16x-16& = &14-6-x \\\Leftrightarrow & 16x \color{red}{-16} & = &8 \color{red}{-x} \\\Leftrightarrow & 16x \color{red}{-16} \color{blue}{+16} \color{blue}{+x} & = &8 \color{red}{-x} \color{blue}{+x} \color{blue}{+16} \\\Leftrightarrow & 16x+x& = &8+16 \\\Leftrightarrow & 17x& = &24 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{24}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{24}{17} & & \\ & V = \left\{ \frac{24}{17} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (4x-4)& = & 15 \color{red}{+} (10+x) \\\Leftrightarrow & 20x-20& = &15+10+x \\\Leftrightarrow & 20x \color{red}{-20} & = &25 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{-20} \color{blue}{+20} \color{blue}{-x} & = &25 \color{red}{+x} \color{blue}{-x} \color{blue}{+20} \\\Leftrightarrow & 20x-x& = &25+20 \\\Leftrightarrow & 19x& = &45 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{45}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{45}{19} & & \\ & V = \left\{ \frac{45}{19} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (-4x+6)& = & -10 \color{red}{+} (8+x) \\\Leftrightarrow & -12x+18& = &-10+8+x \\\Leftrightarrow & -12x \color{red}{+18} & = &-2 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+18} \color{blue}{-18} \color{blue}{-x} & = &-2 \color{red}{+x} \color{blue}{-x} \color{blue}{-18} \\\Leftrightarrow & -12x-x& = &-2-18 \\\Leftrightarrow & -13x& = &-20 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-20}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{20}{13} & & \\ & V = \left\{ \frac{20}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (-5x-5)& = & -13 \color{red}{+} (13+x) \\\Leftrightarrow & -30x-30& = &-13+13+x \\\Leftrightarrow & -30x \color{red}{-30} & = &0 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{-30} \color{blue}{+30} \color{blue}{-x} & = &0 \color{red}{+x} \color{blue}{-x} \color{blue}{+30} \\\Leftrightarrow & -30x-x& = &0+30 \\\Leftrightarrow & -31x& = &30 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{30}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{-30}{31} & & \\ & V = \left\{ \frac{-30}{31} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (-4x-1)& = & 9 \color{red}{+} (10+x) \\\Leftrightarrow & -8x-2& = &9+10+x \\\Leftrightarrow & -8x \color{red}{-2} & = &19 \color{red}{+x} \\\Leftrightarrow & -8x \color{red}{-2} \color{blue}{+2} \color{blue}{-x} & = &19 \color{red}{+x} \color{blue}{-x} \color{blue}{+2} \\\Leftrightarrow & -8x-x& = &19+2 \\\Leftrightarrow & -9x& = &21 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{21}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{-7}{3} & & \\ & V = \left\{ \frac{-7}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (-5x-5)& = & -9 \color{red}{+} (-13-2x) \\\Leftrightarrow & -15x-15& = &-9-13-2x \\\Leftrightarrow & -15x \color{red}{-15} & = &-22 \color{red}{-2x} \\\Leftrightarrow & -15x \color{red}{-15} \color{blue}{+15} \color{blue}{+2x} & = &-22 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+15} \\\Leftrightarrow & -15x+2x& = &-22+15 \\\Leftrightarrow & -13x& = &-7 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-7}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{7}{13} & & \\ & V = \left\{ \frac{7}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (4x-6)& = & 3 \color{red}{-} (12+x) \\\Leftrightarrow & 12x-18& = &3-12-x \\\Leftrightarrow & 12x \color{red}{-18} & = &-9 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-18} \color{blue}{+18} \color{blue}{+x} & = &-9 \color{red}{-x} \color{blue}{+x} \color{blue}{+18} \\\Leftrightarrow & 12x+x& = &-9+18 \\\Leftrightarrow & 13x& = &9 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{9}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{9}{13} & & \\ & V = \left\{ \frac{9}{13} \right\} & \\\end{align}\)