Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (-5x+7)& = & 14 \color{red}{-} (-2+x) \\\Leftrightarrow & -30x+42& = &14+2-x \\\Leftrightarrow & -30x \color{red}{+42} & = &16 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{+42} \color{blue}{-42} \color{blue}{+x} & = &16 \color{red}{-x} \color{blue}{+x} \color{blue}{-42} \\\Leftrightarrow & -30x+x& = &16-42 \\\Leftrightarrow & -29x& = &-26 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{-26}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{26}{29} & & \\ & V = \left\{ \frac{26}{29} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (-4x-4)& = & -1 \color{red}{-} (15+x) \\\Leftrightarrow & -24x-24& = &-1-15-x \\\Leftrightarrow & -24x \color{red}{-24} & = &-16 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{-24} \color{blue}{+24} \color{blue}{+x} & = &-16 \color{red}{-x} \color{blue}{+x} \color{blue}{+24} \\\Leftrightarrow & -24x+x& = &-16+24 \\\Leftrightarrow & -23x& = &8 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{8}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-8}{23} & & \\ & V = \left\{ \frac{-8}{23} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (-6x+3)& = & 9 \color{red}{+} (-8+x) \\\Leftrightarrow & -30x+15& = &9-8+x \\\Leftrightarrow & -30x \color{red}{+15} & = &1 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{+15} \color{blue}{-15} \color{blue}{-x} & = &1 \color{red}{+x} \color{blue}{-x} \color{blue}{-15} \\\Leftrightarrow & -30x-x& = &1-15 \\\Leftrightarrow & -31x& = &-14 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{-14}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{14}{31} & & \\ & V = \left\{ \frac{14}{31} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (6x-2)& = & -5 \color{red}{+} (-6+x) \\\Leftrightarrow & 12x-4& = &-5-6+x \\\Leftrightarrow & 12x \color{red}{-4} & = &-11 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-4} \color{blue}{+4} \color{blue}{-x} & = &-11 \color{red}{+x} \color{blue}{-x} \color{blue}{+4} \\\Leftrightarrow & 12x-x& = &-11+4 \\\Leftrightarrow & 11x& = &-7 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-7}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-7}{11} & & \\ & V = \left\{ \frac{-7}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (3x-1)& = & -1 \color{red}{-} (-15+x) \\\Leftrightarrow & 6x-2& = &-1+15-x \\\Leftrightarrow & 6x \color{red}{-2} & = &14 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{-2} \color{blue}{+2} \color{blue}{+x} & = &14 \color{red}{-x} \color{blue}{+x} \color{blue}{+2} \\\Leftrightarrow & 6x+x& = &14+2 \\\Leftrightarrow & 7x& = &16 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{16}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{16}{7} & & \\ & V = \left\{ \frac{16}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (2x+6)& = & -8 \color{red}{-} (-10-3x) \\\Leftrightarrow & 10x+30& = &-8+10+3x \\\Leftrightarrow & 10x \color{red}{+30} & = &2 \color{red}{+3x} \\\Leftrightarrow & 10x \color{red}{+30} \color{blue}{-30} \color{blue}{-3x} & = &2 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-30} \\\Leftrightarrow & 10x-3x& = &2-30 \\\Leftrightarrow & 7x& = &-28 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-28}{ \color{red}{7} } \\\Leftrightarrow & x = -4 & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (6x-5)& = & -15 \color{red}{-} (4+x) \\\Leftrightarrow & 18x-15& = &-15-4-x \\\Leftrightarrow & 18x \color{red}{-15} & = &-19 \color{red}{-x} \\\Leftrightarrow & 18x \color{red}{-15} \color{blue}{+15} \color{blue}{+x} & = &-19 \color{red}{-x} \color{blue}{+x} \color{blue}{+15} \\\Leftrightarrow & 18x+x& = &-19+15 \\\Leftrightarrow & 19x& = &-4 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-4}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-4}{19} & & \\ & V = \left\{ \frac{-4}{19} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (5x+6)& = & 15 \color{red}{+} (6-3x) \\\Leftrightarrow & 25x+30& = &15+6-3x \\\Leftrightarrow & 25x \color{red}{+30} & = &21 \color{red}{-3x} \\\Leftrightarrow & 25x \color{red}{+30} \color{blue}{-30} \color{blue}{+3x} & = &21 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-30} \\\Leftrightarrow & 25x+3x& = &21-30 \\\Leftrightarrow & 28x& = &-9 \\\Leftrightarrow & \frac{28x}{ \color{red}{28} }& = &\frac{-9}{ \color{red}{28} } \\\Leftrightarrow & x = \frac{-9}{28} & & \\ & V = \left\{ \frac{-9}{28} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (-4x-7)& = & -13 \color{red}{+} (-13+x) \\\Leftrightarrow & -24x-42& = &-13-13+x \\\Leftrightarrow & -24x \color{red}{-42} & = &-26 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{-42} \color{blue}{+42} \color{blue}{-x} & = &-26 \color{red}{+x} \color{blue}{-x} \color{blue}{+42} \\\Leftrightarrow & -24x-x& = &-26+42 \\\Leftrightarrow & -25x& = &16 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{16}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{-16}{25} & & \\ & V = \left\{ \frac{-16}{25} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (6x+2)& = & 13 \color{red}{-} (-14+x) \\\Leftrightarrow & 30x+10& = &13+14-x \\\Leftrightarrow & 30x \color{red}{+10} & = &27 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{+10} \color{blue}{-10} \color{blue}{+x} & = &27 \color{red}{-x} \color{blue}{+x} \color{blue}{-10} \\\Leftrightarrow & 30x+x& = &27-10 \\\Leftrightarrow & 31x& = &17 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{17}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{17}{31} & & \\ & V = \left\{ \frac{17}{31} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (-x-5)& = & 2 \color{red}{-} (13+2x) \\\Leftrightarrow & -3x-15& = &2-13-2x \\\Leftrightarrow & -3x \color{red}{-15} & = &-11 \color{red}{-2x} \\\Leftrightarrow & -3x \color{red}{-15} \color{blue}{+15} \color{blue}{+2x} & = &-11 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+15} \\\Leftrightarrow & -3x+2x& = &-11+15 \\\Leftrightarrow & -x& = &4 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{4}{ \color{red}{-1} } \\\Leftrightarrow & x = -4 & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (-2x-4)& = & -10 \color{red}{-} (14+x) \\\Leftrightarrow & -10x-20& = &-10-14-x \\\Leftrightarrow & -10x \color{red}{-20} & = &-24 \color{red}{-x} \\\Leftrightarrow & -10x \color{red}{-20} \color{blue}{+20} \color{blue}{+x} & = &-24 \color{red}{-x} \color{blue}{+x} \color{blue}{+20} \\\Leftrightarrow & -10x+x& = &-24+20 \\\Leftrightarrow & -9x& = &-4 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{-4}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{4}{9} & & \\ & V = \left\{ \frac{4}{9} \right\} & \\\end{align}\)