Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (-3x-3)& = & -1 \color{red}{+} (9+x) \\\Leftrightarrow & -18x-18& = &-1+9+x \\\Leftrightarrow & -18x \color{red}{-18} & = &8 \color{red}{+x} \\\Leftrightarrow & -18x \color{red}{-18} \color{blue}{+18} \color{blue}{-x} & = &8 \color{red}{+x} \color{blue}{-x} \color{blue}{+18} \\\Leftrightarrow & -18x-x& = &8+18 \\\Leftrightarrow & -19x& = &26 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{26}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-26}{19} & & \\ & V = \left\{ \frac{-26}{19} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (-5x-6)& = & 12 \color{red}{-} (7-3x) \\\Leftrightarrow & -10x-12& = &12-7+3x \\\Leftrightarrow & -10x \color{red}{-12} & = &5 \color{red}{+3x} \\\Leftrightarrow & -10x \color{red}{-12} \color{blue}{+12} \color{blue}{-3x} & = &5 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+12} \\\Leftrightarrow & -10x-3x& = &5+12 \\\Leftrightarrow & -13x& = &17 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{17}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-17}{13} & & \\ & V = \left\{ \frac{-17}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (4x+2)& = & -9 \color{red}{-} (-4+x) \\\Leftrightarrow & 24x+12& = &-9+4-x \\\Leftrightarrow & 24x \color{red}{+12} & = &-5 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &-5 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & 24x+x& = &-5-12 \\\Leftrightarrow & 25x& = &-17 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{-17}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{-17}{25} & & \\ & V = \left\{ \frac{-17}{25} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (2x-7)& = & -4 \color{red}{+} (-10-3x) \\\Leftrightarrow & 10x-35& = &-4-10-3x \\\Leftrightarrow & 10x \color{red}{-35} & = &-14 \color{red}{-3x} \\\Leftrightarrow & 10x \color{red}{-35} \color{blue}{+35} \color{blue}{+3x} & = &-14 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+35} \\\Leftrightarrow & 10x+3x& = &-14+35 \\\Leftrightarrow & 13x& = &21 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{21}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{21}{13} & & \\ & V = \left\{ \frac{21}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (-x-6)& = & -7 \color{red}{-} (2-5x) \\\Leftrightarrow & -6x-36& = &-7-2+5x \\\Leftrightarrow & -6x \color{red}{-36} & = &-9 \color{red}{+5x} \\\Leftrightarrow & -6x \color{red}{-36} \color{blue}{+36} \color{blue}{-5x} & = &-9 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+36} \\\Leftrightarrow & -6x-5x& = &-9+36 \\\Leftrightarrow & -11x& = &27 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{27}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-27}{11} & & \\ & V = \left\{ \frac{-27}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (-5x-2)& = & -1 \color{red}{+} (-1-4x) \\\Leftrightarrow & -25x-10& = &-1-1-4x \\\Leftrightarrow & -25x \color{red}{-10} & = &-2 \color{red}{-4x} \\\Leftrightarrow & -25x \color{red}{-10} \color{blue}{+10} \color{blue}{+4x} & = &-2 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+10} \\\Leftrightarrow & -25x+4x& = &-2+10 \\\Leftrightarrow & -21x& = &8 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{8}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{-8}{21} & & \\ & V = \left\{ \frac{-8}{21} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (3x-7)& = & 2 \color{red}{-} (6-5x) \\\Leftrightarrow & 18x-42& = &2-6+5x \\\Leftrightarrow & 18x \color{red}{-42} & = &-4 \color{red}{+5x} \\\Leftrightarrow & 18x \color{red}{-42} \color{blue}{+42} \color{blue}{-5x} & = &-4 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+42} \\\Leftrightarrow & 18x-5x& = &-4+42 \\\Leftrightarrow & 13x& = &38 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{38}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{38}{13} & & \\ & V = \left\{ \frac{38}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (-x+2)& = & -4 \color{red}{-} (15+x) \\\Leftrightarrow & -5x+10& = &-4-15-x \\\Leftrightarrow & -5x \color{red}{+10} & = &-19 \color{red}{-x} \\\Leftrightarrow & -5x \color{red}{+10} \color{blue}{-10} \color{blue}{+x} & = &-19 \color{red}{-x} \color{blue}{+x} \color{blue}{-10} \\\Leftrightarrow & -5x+x& = &-19-10 \\\Leftrightarrow & -4x& = &-29 \\\Leftrightarrow & \frac{-4x}{ \color{red}{-4} }& = &\frac{-29}{ \color{red}{-4} } \\\Leftrightarrow & x = \frac{29}{4} & & \\ & V = \left\{ \frac{29}{4} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (4x-2)& = & 13 \color{red}{+} (3+x) \\\Leftrightarrow & 16x-8& = &13+3+x \\\Leftrightarrow & 16x \color{red}{-8} & = &16 \color{red}{+x} \\\Leftrightarrow & 16x \color{red}{-8} \color{blue}{+8} \color{blue}{-x} & = &16 \color{red}{+x} \color{blue}{-x} \color{blue}{+8} \\\Leftrightarrow & 16x-x& = &16+8 \\\Leftrightarrow & 15x& = &24 \\\Leftrightarrow & \frac{15x}{ \color{red}{15} }& = &\frac{24}{ \color{red}{15} } \\\Leftrightarrow & x = \frac{8}{5} & & \\ & V = \left\{ \frac{8}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (6x-2)& = & 6 \color{red}{+} (-6+x) \\\Leftrightarrow & 18x-6& = &6-6+x \\\Leftrightarrow & 18x \color{red}{-6} & = &0 \color{red}{+x} \\\Leftrightarrow & 18x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &0 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & 18x-x& = &0+6 \\\Leftrightarrow & 17x& = &6 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{6}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{6}{17} & & \\ & V = \left\{ \frac{6}{17} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (2x+5)& = & 8 \color{red}{-} (-15+x) \\\Leftrightarrow & 6x+15& = &8+15-x \\\Leftrightarrow & 6x \color{red}{+15} & = &23 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{+15} \color{blue}{-15} \color{blue}{+x} & = &23 \color{red}{-x} \color{blue}{+x} \color{blue}{-15} \\\Leftrightarrow & 6x+x& = &23-15 \\\Leftrightarrow & 7x& = &8 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{8}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{8}{7} & & \\ & V = \left\{ \frac{8}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (x+4)& = & 12 \color{red}{+} (-15+3x) \\\Leftrightarrow & 2x+8& = &12-15+3x \\\Leftrightarrow & 2x \color{red}{+8} & = &-3 \color{red}{+3x} \\\Leftrightarrow & 2x \color{red}{+8} \color{blue}{-8} \color{blue}{-3x} & = &-3 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-8} \\\Leftrightarrow & 2x-3x& = &-3-8 \\\Leftrightarrow & -x& = &-11 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-11}{ \color{red}{-1} } \\\Leftrightarrow & x = 11 & & \\ & V = \left\{ 11 \right\} & \\\end{align}\)