Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 8x \color{red}{+8}& = & -7 \color{red}{ +5x } \\\Leftrightarrow & 8x \color{red}{+8}\color{blue}{-8-5x } & = & -7 \color{red}{ +5x }\color{blue}{-8-5x } \\\Leftrightarrow & 8x \color{blue}{-5x } & = & -7 \color{blue}{-8} \\\Leftrightarrow &3x & = &-15\\\Leftrightarrow & \color{red}{3}x & = &-15\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-15}{3} \\\Leftrightarrow & \color{green}{ x = -5 } & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)
2. \(\begin{align} & -8x \color{red}{+4}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+4}\color{blue}{-4-x } & = & -3 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -3 \color{blue}{-4} \\\Leftrightarrow &-9x & = &-7\\\Leftrightarrow & \color{red}{-9}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-7}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{7}{9} } & & \\ & V = \left\{ \frac{7}{9} \right\} & \\\end{align}\)
3. \(\begin{align} & 15x \color{red}{+3}& = & 15 \color{red}{ -2x } \\\Leftrightarrow & 15x \color{red}{+3}\color{blue}{-3+2x } & = & 15 \color{red}{ -2x }\color{blue}{-3+2x } \\\Leftrightarrow & 15x \color{blue}{+2x } & = & 15 \color{blue}{-3} \\\Leftrightarrow &17x & = &12\\\Leftrightarrow & \color{red}{17}x & = &12\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{12}{17} \\\Leftrightarrow & \color{green}{ x = \frac{12}{17} } & & \\ & V = \left\{ \frac{12}{17} \right\} & \\\end{align}\)
4. \(\begin{align} & -14x \color{red}{+2}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+2}\color{blue}{-2-x } & = & -14 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -14 \color{blue}{-2} \\\Leftrightarrow &-15x & = &-16\\\Leftrightarrow & \color{red}{-15}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-16}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{16}{15} } & & \\ & V = \left\{ \frac{16}{15} \right\} & \\\end{align}\)
5. \(\begin{align} & 15x \color{red}{+8}& = & -1 \color{red}{ +4x } \\\Leftrightarrow & 15x \color{red}{+8}\color{blue}{-8-4x } & = & -1 \color{red}{ +4x }\color{blue}{-8-4x } \\\Leftrightarrow & 15x \color{blue}{-4x } & = & -1 \color{blue}{-8} \\\Leftrightarrow &11x & = &-9\\\Leftrightarrow & \color{red}{11}x & = &-9\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-9}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{11} } & & \\ & V = \left\{ \frac{-9}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & -15x \color{red}{+6}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+6}\color{blue}{-6-x } & = & 5 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 5 \color{blue}{-6} \\\Leftrightarrow &-16x & = &-1\\\Leftrightarrow & \color{red}{-16}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-1}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{1}{16} } & & \\ & V = \left\{ \frac{1}{16} \right\} & \\\end{align}\)
7. \(\begin{align} & -11x \color{red}{+3}& = & -9 \color{red}{ +3x } \\\Leftrightarrow & -11x \color{red}{+3}\color{blue}{-3-3x } & = & -9 \color{red}{ +3x }\color{blue}{-3-3x } \\\Leftrightarrow & -11x \color{blue}{-3x } & = & -9 \color{blue}{-3} \\\Leftrightarrow &-14x & = &-12\\\Leftrightarrow & \color{red}{-14}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-12}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{6}{7} } & & \\ & V = \left\{ \frac{6}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & -6x \color{red}{-11}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-11}\color{blue}{+11-x } & = & 13 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 13 \color{blue}{+11} \\\Leftrightarrow &-7x & = &24\\\Leftrightarrow & \color{red}{-7}x & = &24\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{24}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-24}{7} } & & \\ & V = \left\{ \frac{-24}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & -x \color{red}{+2}& = & -3 \color{red}{ +14x } \\\Leftrightarrow & -x \color{red}{+2}\color{blue}{-2-14x } & = & -3 \color{red}{ +14x }\color{blue}{-2-14x } \\\Leftrightarrow & -x \color{blue}{-14x } & = & -3 \color{blue}{-2} \\\Leftrightarrow &-15x & = &-5\\\Leftrightarrow & \color{red}{-15}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-5}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & 9x \color{red}{+1}& = & -2 \color{red}{ +10x } \\\Leftrightarrow & 9x \color{red}{+1}\color{blue}{-1-10x } & = & -2 \color{red}{ +10x }\color{blue}{-1-10x } \\\Leftrightarrow & 9x \color{blue}{-10x } & = & -2 \color{blue}{-1} \\\Leftrightarrow &-x & = &-3\\\Leftrightarrow & \color{red}{-}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-3}{-1} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
11. \(\begin{align} & 3x \color{red}{-2}& = & 5 \color{red}{ -2x } \\\Leftrightarrow & 3x \color{red}{-2}\color{blue}{+2+2x } & = & 5 \color{red}{ -2x }\color{blue}{+2+2x } \\\Leftrightarrow & 3x \color{blue}{+2x } & = & 5 \color{blue}{+2} \\\Leftrightarrow &5x & = &7\\\Leftrightarrow & \color{red}{5}x & = &7\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{7}{5} \\\Leftrightarrow & \color{green}{ x = \frac{7}{5} } & & \\ & V = \left\{ \frac{7}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & 2x \color{red}{+4}& = & 13 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+4}\color{blue}{-4-x } & = & 13 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 13 \color{blue}{-4} \\\Leftrightarrow &x & = &9\\\Leftrightarrow & \color{red}{}x & = &9\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 9 \\\Leftrightarrow & \color{green}{ x = 9 } & & \\ & V = \left\{ 9 \right\} & \\\end{align}\)