Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 9x \color{red}{-3}& = & -1 \color{red}{ +7x } \\\Leftrightarrow & 9x \color{red}{-3}\color{blue}{+3-7x } & = & -1 \color{red}{ +7x }\color{blue}{+3-7x } \\\Leftrightarrow & 9x \color{blue}{-7x } & = & -1 \color{blue}{+3} \\\Leftrightarrow &2x & = &2\\\Leftrightarrow & \color{red}{2}x & = &2\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{2}{2} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
2. \(\begin{align} & -12x \color{red}{-1}& = & 5 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{-1}\color{blue}{+1-13x } & = & 5 \color{red}{ +13x }\color{blue}{+1-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & 5 \color{blue}{+1} \\\Leftrightarrow &-25x & = &6\\\Leftrightarrow & \color{red}{-25}x & = &6\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{6}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{25} } & & \\ & V = \left\{ \frac{-6}{25} \right\} & \\\end{align}\)
3. \(\begin{align} & 4x \color{red}{+2}& = & 6 \color{red}{ +9x } \\\Leftrightarrow & 4x \color{red}{+2}\color{blue}{-2-9x } & = & 6 \color{red}{ +9x }\color{blue}{-2-9x } \\\Leftrightarrow & 4x \color{blue}{-9x } & = & 6 \color{blue}{-2} \\\Leftrightarrow &-5x & = &4\\\Leftrightarrow & \color{red}{-5}x & = &4\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{4}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{5} } & & \\ & V = \left\{ \frac{-4}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & 15x \color{red}{+15}& = & -6 \color{red}{ -7x } \\\Leftrightarrow & 15x \color{red}{+15}\color{blue}{-15+7x } & = & -6 \color{red}{ -7x }\color{blue}{-15+7x } \\\Leftrightarrow & 15x \color{blue}{+7x } & = & -6 \color{blue}{-15} \\\Leftrightarrow &22x & = &-21\\\Leftrightarrow & \color{red}{22}x & = &-21\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{-21}{22} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{22} } & & \\ & V = \left\{ \frac{-21}{22} \right\} & \\\end{align}\)
5. \(\begin{align} & 15x \color{red}{+6}& = & -7 \color{red}{ +x } \\\Leftrightarrow & 15x \color{red}{+6}\color{blue}{-6-x } & = & -7 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & 15x \color{blue}{-x } & = & -7 \color{blue}{-6} \\\Leftrightarrow &14x & = &-13\\\Leftrightarrow & \color{red}{14}x & = &-13\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{-13}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{14} } & & \\ & V = \left\{ \frac{-13}{14} \right\} & \\\end{align}\)
6. \(\begin{align} & 4x \color{red}{+14}& = & 7 \color{red}{ +3x } \\\Leftrightarrow & 4x \color{red}{+14}\color{blue}{-14-3x } & = & 7 \color{red}{ +3x }\color{blue}{-14-3x } \\\Leftrightarrow & 4x \color{blue}{-3x } & = & 7 \color{blue}{-14} \\\Leftrightarrow &x & = &-7\\\Leftrightarrow & \color{red}{}x & = &-7\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -7 \\\Leftrightarrow & \color{green}{ x = -7 } & & \\ & V = \left\{ -7 \right\} & \\\end{align}\)
7. \(\begin{align} & -15x \color{red}{+9}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+9}\color{blue}{-9-x } & = & -12 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -12 \color{blue}{-9} \\\Leftrightarrow &-16x & = &-21\\\Leftrightarrow & \color{red}{-16}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-21}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{21}{16} } & & \\ & V = \left\{ \frac{21}{16} \right\} & \\\end{align}\)
8. \(\begin{align} & x \color{red}{+10}& = & 14 \color{red}{ -4x } \\\Leftrightarrow & x \color{red}{+10}\color{blue}{-10+4x } & = & 14 \color{red}{ -4x }\color{blue}{-10+4x } \\\Leftrightarrow & x \color{blue}{+4x } & = & 14 \color{blue}{-10} \\\Leftrightarrow &5x & = &4\\\Leftrightarrow & \color{red}{5}x & = &4\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{4}{5} \\\Leftrightarrow & \color{green}{ x = \frac{4}{5} } & & \\ & V = \left\{ \frac{4}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & 10x \color{red}{+5}& = & -12 \color{red}{ +13x } \\\Leftrightarrow & 10x \color{red}{+5}\color{blue}{-5-13x } & = & -12 \color{red}{ +13x }\color{blue}{-5-13x } \\\Leftrightarrow & 10x \color{blue}{-13x } & = & -12 \color{blue}{-5} \\\Leftrightarrow &-3x & = &-17\\\Leftrightarrow & \color{red}{-3}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-17}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{17}{3} } & & \\ & V = \left\{ \frac{17}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & -6x \color{red}{+5}& = & 15 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{+5}\color{blue}{-5-13x } & = & 15 \color{red}{ +13x }\color{blue}{-5-13x } \\\Leftrightarrow & -6x \color{blue}{-13x } & = & 15 \color{blue}{-5} \\\Leftrightarrow &-19x & = &10\\\Leftrightarrow & \color{red}{-19}x & = &10\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{10}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{19} } & & \\ & V = \left\{ \frac{-10}{19} \right\} & \\\end{align}\)
11. \(\begin{align} & 9x \color{red}{-7}& = & -8 \color{red}{ +10x } \\\Leftrightarrow & 9x \color{red}{-7}\color{blue}{+7-10x } & = & -8 \color{red}{ +10x }\color{blue}{+7-10x } \\\Leftrightarrow & 9x \color{blue}{-10x } & = & -8 \color{blue}{+7} \\\Leftrightarrow &-x & = &-1\\\Leftrightarrow & \color{red}{-}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-1}{-1} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
12. \(\begin{align} & -3x \color{red}{-13}& = & 12 \color{red}{ +4x } \\\Leftrightarrow & -3x \color{red}{-13}\color{blue}{+13-4x } & = & 12 \color{red}{ +4x }\color{blue}{+13-4x } \\\Leftrightarrow & -3x \color{blue}{-4x } & = & 12 \color{blue}{+13} \\\Leftrightarrow &-7x & = &25\\\Leftrightarrow & \color{red}{-7}x & = &25\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{25}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{7} } & & \\ & V = \left\{ \frac{-25}{7} \right\} & \\\end{align}\)