Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (4x+1)& = & 2 \color{red}{-} (3+x) \\\Leftrightarrow & 20x+5& = &2-3-x \\\Leftrightarrow & 20x \color{red}{+5} & = &-1 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{+5} \color{blue}{-5} \color{blue}{+x} & = &-1 \color{red}{-x} \color{blue}{+x} \color{blue}{-5} \\\Leftrightarrow & 20x+x& = &-1-5 \\\Leftrightarrow & 21x& = &-6 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{-6}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{-2}{7} & & \\ & V = \left\{ \frac{-2}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (-4x-7)& = & 2 \color{red}{-} (-9+x) \\\Leftrightarrow & -20x-35& = &2+9-x \\\Leftrightarrow & -20x \color{red}{-35} & = &11 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{-35} \color{blue}{+35} \color{blue}{+x} & = &11 \color{red}{-x} \color{blue}{+x} \color{blue}{+35} \\\Leftrightarrow & -20x+x& = &11+35 \\\Leftrightarrow & -19x& = &46 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{46}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-46}{19} & & \\ & V = \left\{ \frac{-46}{19} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (6x-4)& = & -3 \color{red}{-} (-7+x) \\\Leftrightarrow & 36x-24& = &-3+7-x \\\Leftrightarrow & 36x \color{red}{-24} & = &4 \color{red}{-x} \\\Leftrightarrow & 36x \color{red}{-24} \color{blue}{+24} \color{blue}{+x} & = &4 \color{red}{-x} \color{blue}{+x} \color{blue}{+24} \\\Leftrightarrow & 36x+x& = &4+24 \\\Leftrightarrow & 37x& = &28 \\\Leftrightarrow & \frac{37x}{ \color{red}{37} }& = &\frac{28}{ \color{red}{37} } \\\Leftrightarrow & x = \frac{28}{37} & & \\ & V = \left\{ \frac{28}{37} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (5x-5)& = & -10 \color{red}{-} (-6-3x) \\\Leftrightarrow & 10x-10& = &-10+6+3x \\\Leftrightarrow & 10x \color{red}{-10} & = &-4 \color{red}{+3x} \\\Leftrightarrow & 10x \color{red}{-10} \color{blue}{+10} \color{blue}{-3x} & = &-4 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+10} \\\Leftrightarrow & 10x-3x& = &-4+10 \\\Leftrightarrow & 7x& = &6 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{6}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{6}{7} & & \\ & V = \left\{ \frac{6}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (4x-2)& = & 2 \color{red}{-} (5+x) \\\Leftrightarrow & 16x-8& = &2-5-x \\\Leftrightarrow & 16x \color{red}{-8} & = &-3 \color{red}{-x} \\\Leftrightarrow & 16x \color{red}{-8} \color{blue}{+8} \color{blue}{+x} & = &-3 \color{red}{-x} \color{blue}{+x} \color{blue}{+8} \\\Leftrightarrow & 16x+x& = &-3+8 \\\Leftrightarrow & 17x& = &5 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{5}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{5}{17} & & \\ & V = \left\{ \frac{5}{17} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (-x-5)& = & 9 \color{red}{-} (-14-3x) \\\Leftrightarrow & -4x-20& = &9+14+3x \\\Leftrightarrow & -4x \color{red}{-20} & = &23 \color{red}{+3x} \\\Leftrightarrow & -4x \color{red}{-20} \color{blue}{+20} \color{blue}{-3x} & = &23 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+20} \\\Leftrightarrow & -4x-3x& = &23+20 \\\Leftrightarrow & -7x& = &43 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{43}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-43}{7} & & \\ & V = \left\{ \frac{-43}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (-x-1)& = & -3 \color{red}{+} (-15-2x) \\\Leftrightarrow & -3x-3& = &-3-15-2x \\\Leftrightarrow & -3x \color{red}{-3} & = &-18 \color{red}{-2x} \\\Leftrightarrow & -3x \color{red}{-3} \color{blue}{+3} \color{blue}{+2x} & = &-18 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+3} \\\Leftrightarrow & -3x+2x& = &-18+3 \\\Leftrightarrow & -x& = &-15 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-15}{ \color{red}{-1} } \\\Leftrightarrow & x = 15 & & \\ & V = \left\{ 15 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (-3x-3)& = & 7 \color{red}{-} (14+4x) \\\Leftrightarrow & -15x-15& = &7-14-4x \\\Leftrightarrow & -15x \color{red}{-15} & = &-7 \color{red}{-4x} \\\Leftrightarrow & -15x \color{red}{-15} \color{blue}{+15} \color{blue}{+4x} & = &-7 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+15} \\\Leftrightarrow & -15x+4x& = &-7+15 \\\Leftrightarrow & -11x& = &8 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{8}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-8}{11} & & \\ & V = \left\{ \frac{-8}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (-5x+5)& = & 11 \color{red}{+} (8-3x) \\\Leftrightarrow & -10x+10& = &11+8-3x \\\Leftrightarrow & -10x \color{red}{+10} & = &19 \color{red}{-3x} \\\Leftrightarrow & -10x \color{red}{+10} \color{blue}{-10} \color{blue}{+3x} & = &19 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-10} \\\Leftrightarrow & -10x+3x& = &19-10 \\\Leftrightarrow & -7x& = &9 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{9}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-9}{7} & & \\ & V = \left\{ \frac{-9}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (x+5)& = & -12 \color{red}{+} (-5+x) \\\Leftrightarrow & 2x+10& = &-12-5+x \\\Leftrightarrow & 2x \color{red}{+10} & = &-17 \color{red}{+x} \\\Leftrightarrow & 2x \color{red}{+10} \color{blue}{-10} \color{blue}{-x} & = &-17 \color{red}{+x} \color{blue}{-x} \color{blue}{-10} \\\Leftrightarrow & 2x-x& = &-17-10 \\\Leftrightarrow & x& = &-27 \\ & V = \left\{ -27 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (-5x-1)& = & -1 \color{red}{-} (-11+x) \\\Leftrightarrow & -30x-6& = &-1+11-x \\\Leftrightarrow & -30x \color{red}{-6} & = &10 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &10 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & -30x+x& = &10+6 \\\Leftrightarrow & -29x& = &16 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{16}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{-16}{29} & & \\ & V = \left\{ \frac{-16}{29} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (-6x-4)& = & -11 \color{red}{+} (1+x) \\\Leftrightarrow & -30x-20& = &-11+1+x \\\Leftrightarrow & -30x \color{red}{-20} & = &-10 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{-20} \color{blue}{+20} \color{blue}{-x} & = &-10 \color{red}{+x} \color{blue}{-x} \color{blue}{+20} \\\Leftrightarrow & -30x-x& = &-10+20 \\\Leftrightarrow & -31x& = &10 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{10}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{-10}{31} & & \\ & V = \left\{ \frac{-10}{31} \right\} & \\\end{align}\)