Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x+\frac{2}{5})& = & 7x+\frac{9}{2} \\\Leftrightarrow & 30x+\frac{12}{5}& = & 7x+\frac{9}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{300}{ \color{blue}{10} }x+ \frac{24}{ \color{blue}{10} })& = & (\frac{70}{ \color{blue}{10} }x+ \frac{45}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 300x \color{red}{+24} & = & \color{red}{70x} +45 \\\Leftrightarrow & 300x \color{red}{+24} \color{blue}{-24} \color{blue}{-70x} & = & \color{red}{70x} +45 \color{blue}{-70x} \color{blue}{-24} \\\Leftrightarrow & 300x-70x& = & 45-24 \\\Leftrightarrow & \color{red}{230} x& = & 21 \\\Leftrightarrow & x = \frac{21}{230} & & \\ & V = \left\{ \frac{21}{230} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x+\frac{3}{8})& = & 7x+\frac{2}{5} \\\Leftrightarrow & 20x-\frac{15}{8}& = & 7x+\frac{2}{5} \\ & & & \text{kgv van noemers 8 en 5 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{800}{ \color{blue}{40} }x- \frac{75}{ \color{blue}{40} })& = & (\frac{280}{ \color{blue}{40} }x+ \frac{16}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 800x \color{red}{-75} & = & \color{red}{280x} +16 \\\Leftrightarrow & 800x \color{red}{-75} \color{blue}{+75} \color{blue}{-280x} & = & \color{red}{280x} +16 \color{blue}{-280x} \color{blue}{+75} \\\Leftrightarrow & 800x-280x& = & 16+75 \\\Leftrightarrow & \color{red}{520} x& = & 91 \\\Leftrightarrow & x = \frac{91}{520} & & \\\Leftrightarrow & x = \frac{7}{40} & & \\ & V = \left\{ \frac{7}{40} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x-\frac{4}{5})& = & 7x+\frac{9}{7} \\\Leftrightarrow & 30x-\frac{24}{5}& = & 7x+\frac{9}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{1050}{ \color{blue}{35} }x- \frac{168}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{45}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 1050x \color{red}{-168} & = & \color{red}{245x} +45 \\\Leftrightarrow & 1050x \color{red}{-168} \color{blue}{+168} \color{blue}{-245x} & = & \color{red}{245x} +45 \color{blue}{-245x} \color{blue}{+168} \\\Leftrightarrow & 1050x-245x& = & 45+168 \\\Leftrightarrow & \color{red}{805} x& = & 213 \\\Leftrightarrow & x = \frac{213}{805} & & \\ & V = \left\{ \frac{213}{805} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x-\frac{4}{9})& = & 5x+\frac{2}{3} \\\Leftrightarrow & 28x-\frac{28}{9}& = & 5x+\frac{2}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{252}{ \color{blue}{9} }x- \frac{28}{ \color{blue}{9} })& = & (\frac{45}{ \color{blue}{9} }x+ \frac{6}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 252x \color{red}{-28} & = & \color{red}{45x} +6 \\\Leftrightarrow & 252x \color{red}{-28} \color{blue}{+28} \color{blue}{-45x} & = & \color{red}{45x} +6 \color{blue}{-45x} \color{blue}{+28} \\\Leftrightarrow & 252x-45x& = & 6+28 \\\Leftrightarrow & \color{red}{207} x& = & 34 \\\Leftrightarrow & x = \frac{34}{207} & & \\ & V = \left\{ \frac{34}{207} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x+\frac{5}{9})& = & 3x+\frac{3}{10} \\\Leftrightarrow & 8x-\frac{20}{9}& = & 3x+\frac{3}{10} \\ & & & \text{kgv van noemers 9 en 10 is 90} \\\Leftrightarrow & \color{blue}{90} .(\frac{720}{ \color{blue}{90} }x- \frac{200}{ \color{blue}{90} })& = & (\frac{270}{ \color{blue}{90} }x+ \frac{27}{ \color{blue}{90} }). \color{blue}{90} \\\Leftrightarrow & 720x \color{red}{-200} & = & \color{red}{270x} +27 \\\Leftrightarrow & 720x \color{red}{-200} \color{blue}{+200} \color{blue}{-270x} & = & \color{red}{270x} +27 \color{blue}{-270x} \color{blue}{+200} \\\Leftrightarrow & 720x-270x& = & 27+200 \\\Leftrightarrow & \color{red}{450} x& = & 227 \\\Leftrightarrow & x = \frac{227}{450} & & \\ & V = \left\{ \frac{227}{450} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x-\frac{4}{11})& = & -7x+\frac{8}{5} \\\Leftrightarrow & 30x+\frac{24}{11}& = & -7x+\frac{8}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{1650}{ \color{blue}{55} }x+ \frac{120}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{88}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 1650x \color{red}{+120} & = & \color{red}{-385x} +88 \\\Leftrightarrow & 1650x \color{red}{+120} \color{blue}{-120} \color{blue}{+385x} & = & \color{red}{-385x} +88 \color{blue}{+385x} \color{blue}{-120} \\\Leftrightarrow & 1650x+385x& = & 88-120 \\\Leftrightarrow & \color{red}{2035} x& = & -32 \\\Leftrightarrow & x = \frac{-32}{2035} & & \\ & V = \left\{ \frac{-32}{2035} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x+\frac{4}{5})& = & -5x+\frac{4}{11} \\\Leftrightarrow & 24x-\frac{24}{5}& = & -5x+\frac{4}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{1320}{ \color{blue}{55} }x- \frac{264}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{20}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 1320x \color{red}{-264} & = & \color{red}{-275x} +20 \\\Leftrightarrow & 1320x \color{red}{-264} \color{blue}{+264} \color{blue}{+275x} & = & \color{red}{-275x} +20 \color{blue}{+275x} \color{blue}{+264} \\\Leftrightarrow & 1320x+275x& = & 20+264 \\\Leftrightarrow & \color{red}{1595} x& = & 284 \\\Leftrightarrow & x = \frac{284}{1595} & & \\ & V = \left\{ \frac{284}{1595} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x+\frac{3}{11})& = & 5x+\frac{10}{3} \\\Leftrightarrow & -12x-\frac{18}{11}& = & 5x+\frac{10}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-396}{ \color{blue}{33} }x- \frac{54}{ \color{blue}{33} })& = & (\frac{165}{ \color{blue}{33} }x+ \frac{110}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -396x \color{red}{-54} & = & \color{red}{165x} +110 \\\Leftrightarrow & -396x \color{red}{-54} \color{blue}{+54} \color{blue}{-165x} & = & \color{red}{165x} +110 \color{blue}{-165x} \color{blue}{+54} \\\Leftrightarrow & -396x-165x& = & 110+54 \\\Leftrightarrow & \color{red}{-561} x& = & 164 \\\Leftrightarrow & x = \frac{164}{-561} & & \\\Leftrightarrow & x = \frac{-164}{561} & & \\ & V = \left\{ \frac{-164}{561} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x+\frac{5}{9})& = & -3x+\frac{6}{5} \\\Leftrightarrow & -14x-\frac{35}{9}& = & -3x+\frac{6}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-630}{ \color{blue}{45} }x- \frac{175}{ \color{blue}{45} })& = & (\frac{-135}{ \color{blue}{45} }x+ \frac{54}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -630x \color{red}{-175} & = & \color{red}{-135x} +54 \\\Leftrightarrow & -630x \color{red}{-175} \color{blue}{+175} \color{blue}{+135x} & = & \color{red}{-135x} +54 \color{blue}{+135x} \color{blue}{+175} \\\Leftrightarrow & -630x+135x& = & 54+175 \\\Leftrightarrow & \color{red}{-495} x& = & 229 \\\Leftrightarrow & x = \frac{229}{-495} & & \\\Leftrightarrow & x = \frac{-229}{495} & & \\ & V = \left\{ \frac{-229}{495} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x+\frac{2}{3})& = & -3x+\frac{5}{7} \\\Leftrightarrow & 28x+\frac{14}{3}& = & -3x+\frac{5}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{588}{ \color{blue}{21} }x+ \frac{98}{ \color{blue}{21} })& = & (\frac{-63}{ \color{blue}{21} }x+ \frac{15}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 588x \color{red}{+98} & = & \color{red}{-63x} +15 \\\Leftrightarrow & 588x \color{red}{+98} \color{blue}{-98} \color{blue}{+63x} & = & \color{red}{-63x} +15 \color{blue}{+63x} \color{blue}{-98} \\\Leftrightarrow & 588x+63x& = & 15-98 \\\Leftrightarrow & \color{red}{651} x& = & -83 \\\Leftrightarrow & x = \frac{-83}{651} & & \\ & V = \left\{ \frac{-83}{651} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x-\frac{2}{11})& = & -9x+\frac{10}{9} \\\Leftrightarrow & -18x-\frac{12}{11}& = & -9x+\frac{10}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-1782}{ \color{blue}{99} }x- \frac{108}{ \color{blue}{99} })& = & (\frac{-891}{ \color{blue}{99} }x+ \frac{110}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -1782x \color{red}{-108} & = & \color{red}{-891x} +110 \\\Leftrightarrow & -1782x \color{red}{-108} \color{blue}{+108} \color{blue}{+891x} & = & \color{red}{-891x} +110 \color{blue}{+891x} \color{blue}{+108} \\\Leftrightarrow & -1782x+891x& = & 110+108 \\\Leftrightarrow & \color{red}{-891} x& = & 218 \\\Leftrightarrow & x = \frac{218}{-891} & & \\\Leftrightarrow & x = \frac{-218}{891} & & \\ & V = \left\{ \frac{-218}{891} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x-\frac{4}{11})& = & -7x+\frac{2}{3} \\\Leftrightarrow & -16x+\frac{16}{11}& = & -7x+\frac{2}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-528}{ \color{blue}{33} }x+ \frac{48}{ \color{blue}{33} })& = & (\frac{-231}{ \color{blue}{33} }x+ \frac{22}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -528x \color{red}{+48} & = & \color{red}{-231x} +22 \\\Leftrightarrow & -528x \color{red}{+48} \color{blue}{-48} \color{blue}{+231x} & = & \color{red}{-231x} +22 \color{blue}{+231x} \color{blue}{-48} \\\Leftrightarrow & -528x+231x& = & 22-48 \\\Leftrightarrow & \color{red}{-297} x& = & -26 \\\Leftrightarrow & x = \frac{-26}{-297} & & \\\Leftrightarrow & x = \frac{26}{297} & & \\ & V = \left\{ \frac{26}{297} \right\} & \\\end{align}\)