Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (x+3)& = & -2 \color{red}{-} (-15+3x) \\\Leftrightarrow & 2x+6& = &-2+15-3x \\\Leftrightarrow & 2x \color{red}{+6} & = &13 \color{red}{-3x} \\\Leftrightarrow & 2x \color{red}{+6} \color{blue}{-6} \color{blue}{+3x} & = &13 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-6} \\\Leftrightarrow & 2x+3x& = &13-6 \\\Leftrightarrow & 5x& = &7 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{7}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{7}{5} & & \\ & V = \left\{ \frac{7}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (x+6)& = & -13 \color{red}{+} (-9-5x) \\\Leftrightarrow & 3x+18& = &-13-9-5x \\\Leftrightarrow & 3x \color{red}{+18} & = &-22 \color{red}{-5x} \\\Leftrightarrow & 3x \color{red}{+18} \color{blue}{-18} \color{blue}{+5x} & = &-22 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-18} \\\Leftrightarrow & 3x+5x& = &-22-18 \\\Leftrightarrow & 8x& = &-40 \\\Leftrightarrow & \frac{8x}{ \color{red}{8} }& = &\frac{-40}{ \color{red}{8} } \\\Leftrightarrow & x = -5 & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (-5x+7)& = & -15 \color{red}{+} (-9+4x) \\\Leftrightarrow & -25x+35& = &-15-9+4x \\\Leftrightarrow & -25x \color{red}{+35} & = &-24 \color{red}{+4x} \\\Leftrightarrow & -25x \color{red}{+35} \color{blue}{-35} \color{blue}{-4x} & = &-24 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-35} \\\Leftrightarrow & -25x-4x& = &-24-35 \\\Leftrightarrow & -29x& = &-59 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{-59}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{59}{29} & & \\ & V = \left\{ \frac{59}{29} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (2x+2)& = & -7 \color{red}{+} (7+x) \\\Leftrightarrow & 10x+10& = &-7+7+x \\\Leftrightarrow & 10x \color{red}{+10} & = &0 \color{red}{+x} \\\Leftrightarrow & 10x \color{red}{+10} \color{blue}{-10} \color{blue}{-x} & = &0 \color{red}{+x} \color{blue}{-x} \color{blue}{-10} \\\Leftrightarrow & 10x-x& = &0-10 \\\Leftrightarrow & 9x& = &-10 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{-10}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{-10}{9} & & \\ & V = \left\{ \frac{-10}{9} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (-4x-6)& = & -11 \color{red}{-} (15+x) \\\Leftrightarrow & -8x-12& = &-11-15-x \\\Leftrightarrow & -8x \color{red}{-12} & = &-26 \color{red}{-x} \\\Leftrightarrow & -8x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &-26 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & -8x+x& = &-26+12 \\\Leftrightarrow & -7x& = &-14 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-14}{ \color{red}{-7} } \\\Leftrightarrow & x = 2 & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (-4x-4)& = & -12 \color{red}{-} (7+x) \\\Leftrightarrow & -24x-24& = &-12-7-x \\\Leftrightarrow & -24x \color{red}{-24} & = &-19 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{-24} \color{blue}{+24} \color{blue}{+x} & = &-19 \color{red}{-x} \color{blue}{+x} \color{blue}{+24} \\\Leftrightarrow & -24x+x& = &-19+24 \\\Leftrightarrow & -23x& = &5 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{5}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-5}{23} & & \\ & V = \left\{ \frac{-5}{23} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (4x-6)& = & -9 \color{red}{+} (-5-5x) \\\Leftrightarrow & 8x-12& = &-9-5-5x \\\Leftrightarrow & 8x \color{red}{-12} & = &-14 \color{red}{-5x} \\\Leftrightarrow & 8x \color{red}{-12} \color{blue}{+12} \color{blue}{+5x} & = &-14 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+12} \\\Leftrightarrow & 8x+5x& = &-14+12 \\\Leftrightarrow & 13x& = &-2 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-2}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-2}{13} & & \\ & V = \left\{ \frac{-2}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (-4x+4)& = & -10 \color{red}{+} (-4+x) \\\Leftrightarrow & -24x+24& = &-10-4+x \\\Leftrightarrow & -24x \color{red}{+24} & = &-14 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{+24} \color{blue}{-24} \color{blue}{-x} & = &-14 \color{red}{+x} \color{blue}{-x} \color{blue}{-24} \\\Leftrightarrow & -24x-x& = &-14-24 \\\Leftrightarrow & -25x& = &-38 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{-38}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{38}{25} & & \\ & V = \left\{ \frac{38}{25} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (-6x+1)& = & -3 \color{red}{-} (9+x) \\\Leftrightarrow & -24x+4& = &-3-9-x \\\Leftrightarrow & -24x \color{red}{+4} & = &-12 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{+4} \color{blue}{-4} \color{blue}{+x} & = &-12 \color{red}{-x} \color{blue}{+x} \color{blue}{-4} \\\Leftrightarrow & -24x+x& = &-12-4 \\\Leftrightarrow & -23x& = &-16 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-16}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{16}{23} & & \\ & V = \left\{ \frac{16}{23} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (x-2)& = & 2 \color{red}{+} (-9+x) \\\Leftrightarrow & 6x-12& = &2-9+x \\\Leftrightarrow & 6x \color{red}{-12} & = &-7 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &-7 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & 6x-x& = &-7+12 \\\Leftrightarrow & 5x& = &5 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{5}{ \color{red}{5} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (4x+5)& = & 13 \color{red}{-} (15+x) \\\Leftrightarrow & 24x+30& = &13-15-x \\\Leftrightarrow & 24x \color{red}{+30} & = &-2 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{+30} \color{blue}{-30} \color{blue}{+x} & = &-2 \color{red}{-x} \color{blue}{+x} \color{blue}{-30} \\\Leftrightarrow & 24x+x& = &-2-30 \\\Leftrightarrow & 25x& = &-32 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{-32}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{-32}{25} & & \\ & V = \left\{ \frac{-32}{25} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (-5x-1)& = & -1 \color{red}{-} (14-2x) \\\Leftrightarrow & -15x-3& = &-1-14+2x \\\Leftrightarrow & -15x \color{red}{-3} & = &-15 \color{red}{+2x} \\\Leftrightarrow & -15x \color{red}{-3} \color{blue}{+3} \color{blue}{-2x} & = &-15 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+3} \\\Leftrightarrow & -15x-2x& = &-15+3 \\\Leftrightarrow & -17x& = &-12 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{-12}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{12}{17} & & \\ & V = \left\{ \frac{12}{17} \right\} & \\\end{align}\)