Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (4x+2)& = & 12 \color{red}{-} (13+x) \\\Leftrightarrow & 20x+10& = &12-13-x \\\Leftrightarrow & 20x \color{red}{+10} & = &-1 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{+10} \color{blue}{-10} \color{blue}{+x} & = &-1 \color{red}{-x} \color{blue}{+x} \color{blue}{-10} \\\Leftrightarrow & 20x+x& = &-1-10 \\\Leftrightarrow & 21x& = &-11 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{-11}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{-11}{21} & & \\ & V = \left\{ \frac{-11}{21} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (x-3)& = & -3 \color{red}{-} (-6+x) \\\Leftrightarrow & 5x-15& = &-3+6-x \\\Leftrightarrow & 5x \color{red}{-15} & = &3 \color{red}{-x} \\\Leftrightarrow & 5x \color{red}{-15} \color{blue}{+15} \color{blue}{+x} & = &3 \color{red}{-x} \color{blue}{+x} \color{blue}{+15} \\\Leftrightarrow & 5x+x& = &3+15 \\\Leftrightarrow & 6x& = &18 \\\Leftrightarrow & \frac{6x}{ \color{red}{6} }& = &\frac{18}{ \color{red}{6} } \\\Leftrightarrow & x = 3 & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (-4x+6)& = & -15 \color{red}{+} (5+x) \\\Leftrightarrow & -8x+12& = &-15+5+x \\\Leftrightarrow & -8x \color{red}{+12} & = &-10 \color{red}{+x} \\\Leftrightarrow & -8x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &-10 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & -8x-x& = &-10-12 \\\Leftrightarrow & -9x& = &-22 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{-22}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{22}{9} & & \\ & V = \left\{ \frac{22}{9} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (2x+5)& = & -4 \color{red}{+} (10+x) \\\Leftrightarrow & 10x+25& = &-4+10+x \\\Leftrightarrow & 10x \color{red}{+25} & = &6 \color{red}{+x} \\\Leftrightarrow & 10x \color{red}{+25} \color{blue}{-25} \color{blue}{-x} & = &6 \color{red}{+x} \color{blue}{-x} \color{blue}{-25} \\\Leftrightarrow & 10x-x& = &6-25 \\\Leftrightarrow & 9x& = &-19 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{-19}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{-19}{9} & & \\ & V = \left\{ \frac{-19}{9} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (6x-3)& = & -4 \color{red}{-} (-7+x) \\\Leftrightarrow & 24x-12& = &-4+7-x \\\Leftrightarrow & 24x \color{red}{-12} & = &3 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &3 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & 24x+x& = &3+12 \\\Leftrightarrow & 25x& = &15 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{15}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{3}{5} & & \\ & V = \left\{ \frac{3}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (-6x-4)& = & 9 \color{red}{-} (-7+x) \\\Leftrightarrow & -30x-20& = &9+7-x \\\Leftrightarrow & -30x \color{red}{-20} & = &16 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{-20} \color{blue}{+20} \color{blue}{+x} & = &16 \color{red}{-x} \color{blue}{+x} \color{blue}{+20} \\\Leftrightarrow & -30x+x& = &16+20 \\\Leftrightarrow & -29x& = &36 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{36}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{-36}{29} & & \\ & V = \left\{ \frac{-36}{29} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (6x-2)& = & -8 \color{red}{-} (14+x) \\\Leftrightarrow & 30x-10& = &-8-14-x \\\Leftrightarrow & 30x \color{red}{-10} & = &-22 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{-10} \color{blue}{+10} \color{blue}{+x} & = &-22 \color{red}{-x} \color{blue}{+x} \color{blue}{+10} \\\Leftrightarrow & 30x+x& = &-22+10 \\\Leftrightarrow & 31x& = &-12 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{-12}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{-12}{31} & & \\ & V = \left\{ \frac{-12}{31} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (6x+2)& = & 3 \color{red}{+} (-9-5x) \\\Leftrightarrow & 18x+6& = &3-9-5x \\\Leftrightarrow & 18x \color{red}{+6} & = &-6 \color{red}{-5x} \\\Leftrightarrow & 18x \color{red}{+6} \color{blue}{-6} \color{blue}{+5x} & = &-6 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-6} \\\Leftrightarrow & 18x+5x& = &-6-6 \\\Leftrightarrow & 23x& = &-12 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-12}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-12}{23} & & \\ & V = \left\{ \frac{-12}{23} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (-x+4)& = & -15 \color{red}{+} (10+x) \\\Leftrightarrow & -4x+16& = &-15+10+x \\\Leftrightarrow & -4x \color{red}{+16} & = &-5 \color{red}{+x} \\\Leftrightarrow & -4x \color{red}{+16} \color{blue}{-16} \color{blue}{-x} & = &-5 \color{red}{+x} \color{blue}{-x} \color{blue}{-16} \\\Leftrightarrow & -4x-x& = &-5-16 \\\Leftrightarrow & -5x& = &-21 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-21}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{21}{5} & & \\ & V = \left\{ \frac{21}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (-5x-5)& = & 5 \color{red}{-} (13-2x) \\\Leftrightarrow & -15x-15& = &5-13+2x \\\Leftrightarrow & -15x \color{red}{-15} & = &-8 \color{red}{+2x} \\\Leftrightarrow & -15x \color{red}{-15} \color{blue}{+15} \color{blue}{-2x} & = &-8 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+15} \\\Leftrightarrow & -15x-2x& = &-8+15 \\\Leftrightarrow & -17x& = &7 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{7}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{-7}{17} & & \\ & V = \left\{ \frac{-7}{17} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (5x-1)& = & -10 \color{red}{-} (13+x) \\\Leftrightarrow & 20x-4& = &-10-13-x \\\Leftrightarrow & 20x \color{red}{-4} & = &-23 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{-4} \color{blue}{+4} \color{blue}{+x} & = &-23 \color{red}{-x} \color{blue}{+x} \color{blue}{+4} \\\Leftrightarrow & 20x+x& = &-23+4 \\\Leftrightarrow & 21x& = &-19 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{-19}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{-19}{21} & & \\ & V = \left\{ \frac{-19}{21} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (-x+5)& = & 11 \color{red}{-} (7+x) \\\Leftrightarrow & -6x+30& = &11-7-x \\\Leftrightarrow & -6x \color{red}{+30} & = &4 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{+30} \color{blue}{-30} \color{blue}{+x} & = &4 \color{red}{-x} \color{blue}{+x} \color{blue}{-30} \\\Leftrightarrow & -6x+x& = &4-30 \\\Leftrightarrow & -5x& = &-26 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-26}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{26}{5} & & \\ & V = \left\{ \frac{26}{5} \right\} & \\\end{align}\)