Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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