Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x+\frac{4}{5})& = & 8x+\frac{2}{9} \\\Leftrightarrow & -21x-\frac{28}{5}& = & 8x+\frac{2}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-945}{ \color{blue}{45} }x- \frac{252}{ \color{blue}{45} })& = & (\frac{360}{ \color{blue}{45} }x+ \frac{10}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -945x \color{red}{-252} & = & \color{red}{360x} +10 \\\Leftrightarrow & -945x \color{red}{-252} \color{blue}{+252} \color{blue}{-360x} & = & \color{red}{360x} +10 \color{blue}{-360x} \color{blue}{+252} \\\Leftrightarrow & -945x-360x& = & 10+252 \\\Leftrightarrow & \color{red}{-1305} x& = & 262 \\\Leftrightarrow & x = \frac{262}{-1305} & & \\\Leftrightarrow & x = \frac{-262}{1305} & & \\ & V = \left\{ \frac{-262}{1305} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x+\frac{3}{10})& = & -5x+\frac{2}{7} \\\Leftrightarrow & -9x+\frac{9}{10}& = & -5x+\frac{2}{7} \\ & & & \text{kgv van noemers 10 en 7 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{-630}{ \color{blue}{70} }x+ \frac{63}{ \color{blue}{70} })& = & (\frac{-350}{ \color{blue}{70} }x+ \frac{20}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & -630x \color{red}{+63} & = & \color{red}{-350x} +20 \\\Leftrightarrow & -630x \color{red}{+63} \color{blue}{-63} \color{blue}{+350x} & = & \color{red}{-350x} +20 \color{blue}{+350x} \color{blue}{-63} \\\Leftrightarrow & -630x+350x& = & 20-63 \\\Leftrightarrow & \color{red}{-280} x& = & -43 \\\Leftrightarrow & x = \frac{-43}{-280} & & \\\Leftrightarrow & x = \frac{43}{280} & & \\ & V = \left\{ \frac{43}{280} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x+\frac{5}{3})& = & -4x+\frac{2}{9} \\\Leftrightarrow & -28x-\frac{35}{3}& = & -4x+\frac{2}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-252}{ \color{blue}{9} }x- \frac{105}{ \color{blue}{9} })& = & (\frac{-36}{ \color{blue}{9} }x+ \frac{2}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -252x \color{red}{-105} & = & \color{red}{-36x} +2 \\\Leftrightarrow & -252x \color{red}{-105} \color{blue}{+105} \color{blue}{+36x} & = & \color{red}{-36x} +2 \color{blue}{+36x} \color{blue}{+105} \\\Leftrightarrow & -252x+36x& = & 2+105 \\\Leftrightarrow & \color{red}{-216} x& = & 107 \\\Leftrightarrow & x = \frac{107}{-216} & & \\\Leftrightarrow & x = \frac{-107}{216} & & \\ & V = \left\{ \frac{-107}{216} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x-\frac{5}{6})& = & 2x+\frac{7}{6} \\\Leftrightarrow & -25x+\frac{25}{6}& = & 2x+\frac{7}{6} \\ & & & \text{kgv van noemers 6 en 6 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-150}{ \color{blue}{6} }x+ \frac{25}{ \color{blue}{6} })& = & (\frac{12}{ \color{blue}{6} }x+ \frac{7}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -150x \color{red}{+25} & = & \color{red}{12x} +7 \\\Leftrightarrow & -150x \color{red}{+25} \color{blue}{-25} \color{blue}{-12x} & = & \color{red}{12x} +7 \color{blue}{-12x} \color{blue}{-25} \\\Leftrightarrow & -150x-12x& = & 7-25 \\\Leftrightarrow & \color{red}{-162} x& = & -18 \\\Leftrightarrow & x = \frac{-18}{-162} & & \\\Leftrightarrow & x = \frac{1}{9} & & \\ & V = \left\{ \frac{1}{9} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x+\frac{5}{8})& = & -7x+\frac{4}{9} \\\Leftrightarrow & -6x-\frac{15}{8}& = & -7x+\frac{4}{9} \\ & & & \text{kgv van noemers 8 en 9 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{-432}{ \color{blue}{72} }x- \frac{135}{ \color{blue}{72} })& = & (\frac{-504}{ \color{blue}{72} }x+ \frac{32}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & -432x \color{red}{-135} & = & \color{red}{-504x} +32 \\\Leftrightarrow & -432x \color{red}{-135} \color{blue}{+135} \color{blue}{+504x} & = & \color{red}{-504x} +32 \color{blue}{+504x} \color{blue}{+135} \\\Leftrightarrow & -432x+504x& = & 32+135 \\\Leftrightarrow & \color{red}{72} x& = & 167 \\\Leftrightarrow & x = \frac{167}{72} & & \\ & V = \left\{ \frac{167}{72} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x-\frac{2}{9})& = & -3x+\frac{3}{10} \\\Leftrightarrow & -8x+\frac{8}{9}& = & -3x+\frac{3}{10} \\ & & & \text{kgv van noemers 9 en 10 is 90} \\\Leftrightarrow & \color{blue}{90} .(\frac{-720}{ \color{blue}{90} }x+ \frac{80}{ \color{blue}{90} })& = & (\frac{-270}{ \color{blue}{90} }x+ \frac{27}{ \color{blue}{90} }). \color{blue}{90} \\\Leftrightarrow & -720x \color{red}{+80} & = & \color{red}{-270x} +27 \\\Leftrightarrow & -720x \color{red}{+80} \color{blue}{-80} \color{blue}{+270x} & = & \color{red}{-270x} +27 \color{blue}{+270x} \color{blue}{-80} \\\Leftrightarrow & -720x+270x& = & 27-80 \\\Leftrightarrow & \color{red}{-450} x& = & -53 \\\Leftrightarrow & x = \frac{-53}{-450} & & \\\Leftrightarrow & x = \frac{53}{450} & & \\ & V = \left\{ \frac{53}{450} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x+\frac{3}{5})& = & 7x+\frac{6}{5} \\\Leftrightarrow & 30x+\frac{18}{5}& = & 7x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{150}{ \color{blue}{5} }x+ \frac{18}{ \color{blue}{5} })& = & (\frac{35}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 150x \color{red}{+18} & = & \color{red}{35x} +6 \\\Leftrightarrow & 150x \color{red}{+18} \color{blue}{-18} \color{blue}{-35x} & = & \color{red}{35x} +6 \color{blue}{-35x} \color{blue}{-18} \\\Leftrightarrow & 150x-35x& = & 6-18 \\\Leftrightarrow & \color{red}{115} x& = & -12 \\\Leftrightarrow & x = \frac{-12}{115} & & \\ & V = \left\{ \frac{-12}{115} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x+\frac{4}{5})& = & 7x+\frac{7}{4} \\\Leftrightarrow & -16x+\frac{16}{5}& = & 7x+\frac{7}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-320}{ \color{blue}{20} }x+ \frac{64}{ \color{blue}{20} })& = & (\frac{140}{ \color{blue}{20} }x+ \frac{35}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -320x \color{red}{+64} & = & \color{red}{140x} +35 \\\Leftrightarrow & -320x \color{red}{+64} \color{blue}{-64} \color{blue}{-140x} & = & \color{red}{140x} +35 \color{blue}{-140x} \color{blue}{-64} \\\Leftrightarrow & -320x-140x& = & 35-64 \\\Leftrightarrow & \color{red}{-460} x& = & -29 \\\Leftrightarrow & x = \frac{-29}{-460} & & \\\Leftrightarrow & x = \frac{29}{460} & & \\ & V = \left\{ \frac{29}{460} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x-\frac{5}{11})& = & -7x+\frac{10}{11} \\\Leftrightarrow & 6x-\frac{15}{11}& = & -7x+\frac{10}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{66}{ \color{blue}{11} }x- \frac{15}{ \color{blue}{11} })& = & (\frac{-77}{ \color{blue}{11} }x+ \frac{10}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 66x \color{red}{-15} & = & \color{red}{-77x} +10 \\\Leftrightarrow & 66x \color{red}{-15} \color{blue}{+15} \color{blue}{+77x} & = & \color{red}{-77x} +10 \color{blue}{+77x} \color{blue}{+15} \\\Leftrightarrow & 66x+77x& = & 10+15 \\\Leftrightarrow & \color{red}{143} x& = & 25 \\\Leftrightarrow & x = \frac{25}{143} & & \\ & V = \left\{ \frac{25}{143} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x+\frac{4}{7})& = & -7x+\frac{5}{6} \\\Leftrightarrow & -10x-\frac{20}{7}& = & -7x+\frac{5}{6} \\ & & & \text{kgv van noemers 7 en 6 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{-420}{ \color{blue}{42} }x- \frac{120}{ \color{blue}{42} })& = & (\frac{-294}{ \color{blue}{42} }x+ \frac{35}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & -420x \color{red}{-120} & = & \color{red}{-294x} +35 \\\Leftrightarrow & -420x \color{red}{-120} \color{blue}{+120} \color{blue}{+294x} & = & \color{red}{-294x} +35 \color{blue}{+294x} \color{blue}{+120} \\\Leftrightarrow & -420x+294x& = & 35+120 \\\Leftrightarrow & \color{red}{-126} x& = & 155 \\\Leftrightarrow & x = \frac{155}{-126} & & \\\Leftrightarrow & x = \frac{-155}{126} & & \\ & V = \left\{ \frac{-155}{126} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x-\frac{2}{7})& = & -7x+\frac{10}{7} \\\Leftrightarrow & -10x+\frac{10}{7}& = & -7x+\frac{10}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-70}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} })& = & (\frac{-49}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -70x \color{red}{+10} & = & \color{red}{-49x} +10 \\\Leftrightarrow & -70x \color{red}{+10} \color{blue}{-10} \color{blue}{+49x} & = & \color{red}{-49x} +10 \color{blue}{+49x} \color{blue}{-10} \\\Leftrightarrow & -70x+49x& = & 10-10 \\\Leftrightarrow & \color{red}{-21} x& = & 0 \\\Leftrightarrow & x = \frac{0}{-21} & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x+\frac{2}{9})& = & -7x+\frac{6}{11} \\\Leftrightarrow & -16x-\frac{8}{9}& = & -7x+\frac{6}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-1584}{ \color{blue}{99} }x- \frac{88}{ \color{blue}{99} })& = & (\frac{-693}{ \color{blue}{99} }x+ \frac{54}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -1584x \color{red}{-88} & = & \color{red}{-693x} +54 \\\Leftrightarrow & -1584x \color{red}{-88} \color{blue}{+88} \color{blue}{+693x} & = & \color{red}{-693x} +54 \color{blue}{+693x} \color{blue}{+88} \\\Leftrightarrow & -1584x+693x& = & 54+88 \\\Leftrightarrow & \color{red}{-891} x& = & 142 \\\Leftrightarrow & x = \frac{142}{-891} & & \\\Leftrightarrow & x = \frac{-142}{891} & & \\ & V = \left\{ \frac{-142}{891} \right\} & \\\end{align}\)