Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (5x-3)& = & 7 \color{red}{-} (-5-2x) \\\Leftrightarrow & 15x-9& = &7+5+2x \\\Leftrightarrow & 15x \color{red}{-9} & = &12 \color{red}{+2x} \\\Leftrightarrow & 15x \color{red}{-9} \color{blue}{+9} \color{blue}{-2x} & = &12 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+9} \\\Leftrightarrow & 15x-2x& = &12+9 \\\Leftrightarrow & 13x& = &21 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{21}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{21}{13} & & \\ & V = \left\{ \frac{21}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (2x-7)& = & -12 \color{red}{+} (-10-3x) \\\Leftrightarrow & 10x-35& = &-12-10-3x \\\Leftrightarrow & 10x \color{red}{-35} & = &-22 \color{red}{-3x} \\\Leftrightarrow & 10x \color{red}{-35} \color{blue}{+35} \color{blue}{+3x} & = &-22 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+35} \\\Leftrightarrow & 10x+3x& = &-22+35 \\\Leftrightarrow & 13x& = &13 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{13}{ \color{red}{13} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (5x+6)& = & 15 \color{red}{-} (1+x) \\\Leftrightarrow & 20x+24& = &15-1-x \\\Leftrightarrow & 20x \color{red}{+24} & = &14 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{+24} \color{blue}{-24} \color{blue}{+x} & = &14 \color{red}{-x} \color{blue}{+x} \color{blue}{-24} \\\Leftrightarrow & 20x+x& = &14-24 \\\Leftrightarrow & 21x& = &-10 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{-10}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{-10}{21} & & \\ & V = \left\{ \frac{-10}{21} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (5x+4)& = & 1 \color{red}{-} (1-4x) \\\Leftrightarrow & 25x+20& = &1-1+4x \\\Leftrightarrow & 25x \color{red}{+20} & = &0 \color{red}{+4x} \\\Leftrightarrow & 25x \color{red}{+20} \color{blue}{-20} \color{blue}{-4x} & = &0 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-20} \\\Leftrightarrow & 25x-4x& = &0-20 \\\Leftrightarrow & 21x& = &-20 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{-20}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{-20}{21} & & \\ & V = \left\{ \frac{-20}{21} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (2x+3)& = & 1 \color{red}{-} (12-5x) \\\Leftrightarrow & 6x+9& = &1-12+5x \\\Leftrightarrow & 6x \color{red}{+9} & = &-11 \color{red}{+5x} \\\Leftrightarrow & 6x \color{red}{+9} \color{blue}{-9} \color{blue}{-5x} & = &-11 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-9} \\\Leftrightarrow & 6x-5x& = &-11-9 \\\Leftrightarrow & x& = &-20 \\ & V = \left\{ -20 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (-3x+4)& = & -12 \color{red}{-} (-2+x) \\\Leftrightarrow & -18x+24& = &-12+2-x \\\Leftrightarrow & -18x \color{red}{+24} & = &-10 \color{red}{-x} \\\Leftrightarrow & -18x \color{red}{+24} \color{blue}{-24} \color{blue}{+x} & = &-10 \color{red}{-x} \color{blue}{+x} \color{blue}{-24} \\\Leftrightarrow & -18x+x& = &-10-24 \\\Leftrightarrow & -17x& = &-34 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{-34}{ \color{red}{-17} } \\\Leftrightarrow & x = 2 & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (3x+6)& = & -15 \color{red}{+} (9+x) \\\Leftrightarrow & 18x+36& = &-15+9+x \\\Leftrightarrow & 18x \color{red}{+36} & = &-6 \color{red}{+x} \\\Leftrightarrow & 18x \color{red}{+36} \color{blue}{-36} \color{blue}{-x} & = &-6 \color{red}{+x} \color{blue}{-x} \color{blue}{-36} \\\Leftrightarrow & 18x-x& = &-6-36 \\\Leftrightarrow & 17x& = &-42 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{-42}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{-42}{17} & & \\ & V = \left\{ \frac{-42}{17} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (-3x-3)& = & -15 \color{red}{-} (-8-4x) \\\Leftrightarrow & -9x-9& = &-15+8+4x \\\Leftrightarrow & -9x \color{red}{-9} & = &-7 \color{red}{+4x} \\\Leftrightarrow & -9x \color{red}{-9} \color{blue}{+9} \color{blue}{-4x} & = &-7 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+9} \\\Leftrightarrow & -9x-4x& = &-7+9 \\\Leftrightarrow & -13x& = &2 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{2}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-2}{13} & & \\ & V = \left\{ \frac{-2}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (3x+4)& = & -2 \color{red}{+} (1-5x) \\\Leftrightarrow & 18x+24& = &-2+1-5x \\\Leftrightarrow & 18x \color{red}{+24} & = &-1 \color{red}{-5x} \\\Leftrightarrow & 18x \color{red}{+24} \color{blue}{-24} \color{blue}{+5x} & = &-1 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-24} \\\Leftrightarrow & 18x+5x& = &-1-24 \\\Leftrightarrow & 23x& = &-25 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-25}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-25}{23} & & \\ & V = \left\{ \frac{-25}{23} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (3x+7)& = & 4 \color{red}{+} (-10+x) \\\Leftrightarrow & 15x+35& = &4-10+x \\\Leftrightarrow & 15x \color{red}{+35} & = &-6 \color{red}{+x} \\\Leftrightarrow & 15x \color{red}{+35} \color{blue}{-35} \color{blue}{-x} & = &-6 \color{red}{+x} \color{blue}{-x} \color{blue}{-35} \\\Leftrightarrow & 15x-x& = &-6-35 \\\Leftrightarrow & 14x& = &-41 \\\Leftrightarrow & \frac{14x}{ \color{red}{14} }& = &\frac{-41}{ \color{red}{14} } \\\Leftrightarrow & x = \frac{-41}{14} & & \\ & V = \left\{ \frac{-41}{14} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (2x+6)& = & 4 \color{red}{-} (-2-3x) \\\Leftrightarrow & 10x+30& = &4+2+3x \\\Leftrightarrow & 10x \color{red}{+30} & = &6 \color{red}{+3x} \\\Leftrightarrow & 10x \color{red}{+30} \color{blue}{-30} \color{blue}{-3x} & = &6 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-30} \\\Leftrightarrow & 10x-3x& = &6-30 \\\Leftrightarrow & 7x& = &-24 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-24}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-24}{7} & & \\ & V = \left\{ \frac{-24}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (-2x-7)& = & 7 \color{red}{-} (-6-5x) \\\Leftrightarrow & -6x-21& = &7+6+5x \\\Leftrightarrow & -6x \color{red}{-21} & = &13 \color{red}{+5x} \\\Leftrightarrow & -6x \color{red}{-21} \color{blue}{+21} \color{blue}{-5x} & = &13 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+21} \\\Leftrightarrow & -6x-5x& = &13+21 \\\Leftrightarrow & -11x& = &34 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{34}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-34}{11} & & \\ & V = \left\{ \frac{-34}{11} \right\} & \\\end{align}\)