Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (4x+6)& = & -6 \color{red}{-} (-1+x) \\\Leftrightarrow & 8x+12& = &-6+1-x \\\Leftrightarrow & 8x \color{red}{+12} & = &-5 \color{red}{-x} \\\Leftrightarrow & 8x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &-5 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & 8x+x& = &-5-12 \\\Leftrightarrow & 9x& = &-17 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{-17}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{-17}{9} & & \\ & V = \left\{ \frac{-17}{9} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (-5x-7)& = & -14 \color{red}{-} (-6+3x) \\\Leftrightarrow & -10x-14& = &-14+6-3x \\\Leftrightarrow & -10x \color{red}{-14} & = &-8 \color{red}{-3x} \\\Leftrightarrow & -10x \color{red}{-14} \color{blue}{+14} \color{blue}{+3x} & = &-8 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+14} \\\Leftrightarrow & -10x+3x& = &-8+14 \\\Leftrightarrow & -7x& = &6 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{6}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-6}{7} & & \\ & V = \left\{ \frac{-6}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (5x-7)& = & -13 \color{red}{-} (-15-2x) \\\Leftrightarrow & 15x-21& = &-13+15+2x \\\Leftrightarrow & 15x \color{red}{-21} & = &2 \color{red}{+2x} \\\Leftrightarrow & 15x \color{red}{-21} \color{blue}{+21} \color{blue}{-2x} & = &2 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+21} \\\Leftrightarrow & 15x-2x& = &2+21 \\\Leftrightarrow & 13x& = &23 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{23}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{23}{13} & & \\ & V = \left\{ \frac{23}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (5x-5)& = & -7 \color{red}{+} (-12+x) \\\Leftrightarrow & 10x-10& = &-7-12+x \\\Leftrightarrow & 10x \color{red}{-10} & = &-19 \color{red}{+x} \\\Leftrightarrow & 10x \color{red}{-10} \color{blue}{+10} \color{blue}{-x} & = &-19 \color{red}{+x} \color{blue}{-x} \color{blue}{+10} \\\Leftrightarrow & 10x-x& = &-19+10 \\\Leftrightarrow & 9x& = &-9 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{-9}{ \color{red}{9} } \\\Leftrightarrow & x = -1 & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (-2x-1)& = & -10 \color{red}{-} (-2+3x) \\\Leftrightarrow & -10x-5& = &-10+2-3x \\\Leftrightarrow & -10x \color{red}{-5} & = &-8 \color{red}{-3x} \\\Leftrightarrow & -10x \color{red}{-5} \color{blue}{+5} \color{blue}{+3x} & = &-8 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+5} \\\Leftrightarrow & -10x+3x& = &-8+5 \\\Leftrightarrow & -7x& = &-3 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-3}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{3}{7} & & \\ & V = \left\{ \frac{3}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (3x-7)& = & -6 \color{red}{-} (6+x) \\\Leftrightarrow & 15x-35& = &-6-6-x \\\Leftrightarrow & 15x \color{red}{-35} & = &-12 \color{red}{-x} \\\Leftrightarrow & 15x \color{red}{-35} \color{blue}{+35} \color{blue}{+x} & = &-12 \color{red}{-x} \color{blue}{+x} \color{blue}{+35} \\\Leftrightarrow & 15x+x& = &-12+35 \\\Leftrightarrow & 16x& = &23 \\\Leftrightarrow & \frac{16x}{ \color{red}{16} }& = &\frac{23}{ \color{red}{16} } \\\Leftrightarrow & x = \frac{23}{16} & & \\ & V = \left\{ \frac{23}{16} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (3x+3)& = & -5 \color{red}{-} (6-4x) \\\Leftrightarrow & 9x+9& = &-5-6+4x \\\Leftrightarrow & 9x \color{red}{+9} & = &-11 \color{red}{+4x} \\\Leftrightarrow & 9x \color{red}{+9} \color{blue}{-9} \color{blue}{-4x} & = &-11 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-9} \\\Leftrightarrow & 9x-4x& = &-11-9 \\\Leftrightarrow & 5x& = &-20 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-20}{ \color{red}{5} } \\\Leftrightarrow & x = -4 & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (5x-4)& = & 9 \color{red}{+} (12+x) \\\Leftrightarrow & 10x-8& = &9+12+x \\\Leftrightarrow & 10x \color{red}{-8} & = &21 \color{red}{+x} \\\Leftrightarrow & 10x \color{red}{-8} \color{blue}{+8} \color{blue}{-x} & = &21 \color{red}{+x} \color{blue}{-x} \color{blue}{+8} \\\Leftrightarrow & 10x-x& = &21+8 \\\Leftrightarrow & 9x& = &29 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{29}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{29}{9} & & \\ & V = \left\{ \frac{29}{9} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (2x-5)& = & -10 \color{red}{-} (8+x) \\\Leftrightarrow & 12x-30& = &-10-8-x \\\Leftrightarrow & 12x \color{red}{-30} & = &-18 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-30} \color{blue}{+30} \color{blue}{+x} & = &-18 \color{red}{-x} \color{blue}{+x} \color{blue}{+30} \\\Leftrightarrow & 12x+x& = &-18+30 \\\Leftrightarrow & 13x& = &12 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{12}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{12}{13} & & \\ & V = \left\{ \frac{12}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (-5x-5)& = & 2 \color{red}{-} (-4-2x) \\\Leftrightarrow & -15x-15& = &2+4+2x \\\Leftrightarrow & -15x \color{red}{-15} & = &6 \color{red}{+2x} \\\Leftrightarrow & -15x \color{red}{-15} \color{blue}{+15} \color{blue}{-2x} & = &6 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+15} \\\Leftrightarrow & -15x-2x& = &6+15 \\\Leftrightarrow & -17x& = &21 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{21}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{-21}{17} & & \\ & V = \left\{ \frac{-21}{17} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (2x-4)& = & 11 \color{red}{+} (-11+x) \\\Leftrightarrow & 4x-8& = &11-11+x \\\Leftrightarrow & 4x \color{red}{-8} & = &0 \color{red}{+x} \\\Leftrightarrow & 4x \color{red}{-8} \color{blue}{+8} \color{blue}{-x} & = &0 \color{red}{+x} \color{blue}{-x} \color{blue}{+8} \\\Leftrightarrow & 4x-x& = &0+8 \\\Leftrightarrow & 3x& = &8 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{8}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{8}{3} & & \\ & V = \left\{ \frac{8}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (-3x-2)& = & -7 \color{red}{-} (12+4x) \\\Leftrightarrow & -9x-6& = &-7-12-4x \\\Leftrightarrow & -9x \color{red}{-6} & = &-19 \color{red}{-4x} \\\Leftrightarrow & -9x \color{red}{-6} \color{blue}{+6} \color{blue}{+4x} & = &-19 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+6} \\\Leftrightarrow & -9x+4x& = &-19+6 \\\Leftrightarrow & -5x& = &-13 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-13}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{13}{5} & & \\ & V = \left\{ \frac{13}{5} \right\} & \\\end{align}\)