Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (-3x-3)& = & -3 \color{red}{+} (15-4x) \\\Leftrightarrow & -9x-9& = &-3+15-4x \\\Leftrightarrow & -9x \color{red}{-9} & = &12 \color{red}{-4x} \\\Leftrightarrow & -9x \color{red}{-9} \color{blue}{+9} \color{blue}{+4x} & = &12 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+9} \\\Leftrightarrow & -9x+4x& = &12+9 \\\Leftrightarrow & -5x& = &21 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{21}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-21}{5} & & \\ & V = \left\{ \frac{-21}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (-2x+6)& = & -5 \color{red}{+} (-9+x) \\\Leftrightarrow & -10x+30& = &-5-9+x \\\Leftrightarrow & -10x \color{red}{+30} & = &-14 \color{red}{+x} \\\Leftrightarrow & -10x \color{red}{+30} \color{blue}{-30} \color{blue}{-x} & = &-14 \color{red}{+x} \color{blue}{-x} \color{blue}{-30} \\\Leftrightarrow & -10x-x& = &-14-30 \\\Leftrightarrow & -11x& = &-44 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-44}{ \color{red}{-11} } \\\Leftrightarrow & x = 4 & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (5x-6)& = & -2 \color{red}{+} (-14+x) \\\Leftrightarrow & 15x-18& = &-2-14+x \\\Leftrightarrow & 15x \color{red}{-18} & = &-16 \color{red}{+x} \\\Leftrightarrow & 15x \color{red}{-18} \color{blue}{+18} \color{blue}{-x} & = &-16 \color{red}{+x} \color{blue}{-x} \color{blue}{+18} \\\Leftrightarrow & 15x-x& = &-16+18 \\\Leftrightarrow & 14x& = &2 \\\Leftrightarrow & \frac{14x}{ \color{red}{14} }& = &\frac{2}{ \color{red}{14} } \\\Leftrightarrow & x = \frac{1}{7} & & \\ & V = \left\{ \frac{1}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (-2x+4)& = & -4 \color{red}{+} (5+x) \\\Leftrightarrow & -12x+24& = &-4+5+x \\\Leftrightarrow & -12x \color{red}{+24} & = &1 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+24} \color{blue}{-24} \color{blue}{-x} & = &1 \color{red}{+x} \color{blue}{-x} \color{blue}{-24} \\\Leftrightarrow & -12x-x& = &1-24 \\\Leftrightarrow & -13x& = &-23 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-23}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{23}{13} & & \\ & V = \left\{ \frac{23}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (5x-7)& = & -3 \color{red}{-} (-5+x) \\\Leftrightarrow & 25x-35& = &-3+5-x \\\Leftrightarrow & 25x \color{red}{-35} & = &2 \color{red}{-x} \\\Leftrightarrow & 25x \color{red}{-35} \color{blue}{+35} \color{blue}{+x} & = &2 \color{red}{-x} \color{blue}{+x} \color{blue}{+35} \\\Leftrightarrow & 25x+x& = &2+35 \\\Leftrightarrow & 26x& = &37 \\\Leftrightarrow & \frac{26x}{ \color{red}{26} }& = &\frac{37}{ \color{red}{26} } \\\Leftrightarrow & x = \frac{37}{26} & & \\ & V = \left\{ \frac{37}{26} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (-6x-2)& = & 2 \color{red}{+} (3-5x) \\\Leftrightarrow & -18x-6& = &2+3-5x \\\Leftrightarrow & -18x \color{red}{-6} & = &5 \color{red}{-5x} \\\Leftrightarrow & -18x \color{red}{-6} \color{blue}{+6} \color{blue}{+5x} & = &5 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+6} \\\Leftrightarrow & -18x+5x& = &5+6 \\\Leftrightarrow & -13x& = &11 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{11}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-11}{13} & & \\ & V = \left\{ \frac{-11}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (-6x+7)& = & 13 \color{red}{+} (-13+x) \\\Leftrightarrow & -24x+28& = &13-13+x \\\Leftrightarrow & -24x \color{red}{+28} & = &0 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{+28} \color{blue}{-28} \color{blue}{-x} & = &0 \color{red}{+x} \color{blue}{-x} \color{blue}{-28} \\\Leftrightarrow & -24x-x& = &0-28 \\\Leftrightarrow & -25x& = &-28 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{-28}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{28}{25} & & \\ & V = \left\{ \frac{28}{25} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (-4x-7)& = & 15 \color{red}{-} (9+x) \\\Leftrightarrow & -24x-42& = &15-9-x \\\Leftrightarrow & -24x \color{red}{-42} & = &6 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{-42} \color{blue}{+42} \color{blue}{+x} & = &6 \color{red}{-x} \color{blue}{+x} \color{blue}{+42} \\\Leftrightarrow & -24x+x& = &6+42 \\\Leftrightarrow & -23x& = &48 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{48}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-48}{23} & & \\ & V = \left\{ \frac{-48}{23} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (-4x+7)& = & 15 \color{red}{+} (-11+x) \\\Leftrightarrow & -12x+21& = &15-11+x \\\Leftrightarrow & -12x \color{red}{+21} & = &4 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+21} \color{blue}{-21} \color{blue}{-x} & = &4 \color{red}{+x} \color{blue}{-x} \color{blue}{-21} \\\Leftrightarrow & -12x-x& = &4-21 \\\Leftrightarrow & -13x& = &-17 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-17}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{17}{13} & & \\ & V = \left\{ \frac{17}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (2x-6)& = & -6 \color{red}{+} (11+x) \\\Leftrightarrow & 8x-24& = &-6+11+x \\\Leftrightarrow & 8x \color{red}{-24} & = &5 \color{red}{+x} \\\Leftrightarrow & 8x \color{red}{-24} \color{blue}{+24} \color{blue}{-x} & = &5 \color{red}{+x} \color{blue}{-x} \color{blue}{+24} \\\Leftrightarrow & 8x-x& = &5+24 \\\Leftrightarrow & 7x& = &29 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{29}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{29}{7} & & \\ & V = \left\{ \frac{29}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (2x-5)& = & -6 \color{red}{+} (7-3x) \\\Leftrightarrow & 4x-10& = &-6+7-3x \\\Leftrightarrow & 4x \color{red}{-10} & = &1 \color{red}{-3x} \\\Leftrightarrow & 4x \color{red}{-10} \color{blue}{+10} \color{blue}{+3x} & = &1 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+10} \\\Leftrightarrow & 4x+3x& = &1+10 \\\Leftrightarrow & 7x& = &11 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{11}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{11}{7} & & \\ & V = \left\{ \frac{11}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (6x+7)& = & -5 \color{red}{-} (-11+x) \\\Leftrightarrow & 30x+35& = &-5+11-x \\\Leftrightarrow & 30x \color{red}{+35} & = &6 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{+35} \color{blue}{-35} \color{blue}{+x} & = &6 \color{red}{-x} \color{blue}{+x} \color{blue}{-35} \\\Leftrightarrow & 30x+x& = &6-35 \\\Leftrightarrow & 31x& = &-29 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{-29}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{-29}{31} & & \\ & V = \left\{ \frac{-29}{31} \right\} & \\\end{align}\)