Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x-1)& = & -9x+\frac{5}{2} \\\Leftrightarrow & 10x+5& = & -9x+\frac{5}{2} \\ & & & \text{kgv van noemers 1 en 2 is 2} \\\Leftrightarrow & \color{blue}{2} .(\frac{20}{ \color{blue}{2} }x+ \frac{10}{ \color{blue}{2} })& = & (\frac{-18}{ \color{blue}{2} }x+ \frac{5}{ \color{blue}{2} }). \color{blue}{2} \\\Leftrightarrow & 20x \color{red}{+10} & = & \color{red}{-18x} +5 \\\Leftrightarrow & 20x \color{red}{+10} \color{blue}{-10} \color{blue}{+18x} & = & \color{red}{-18x} +5 \color{blue}{+18x} \color{blue}{-10} \\\Leftrightarrow & 20x+18x& = & 5-10 \\\Leftrightarrow & \color{red}{38} x& = & -5 \\\Leftrightarrow & x = \frac{-5}{38} & & \\ & V = \left\{ \frac{-5}{38} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x+\frac{3}{5})& = & -9x+\frac{5}{9} \\\Leftrightarrow & 20x+\frac{12}{5}& = & -9x+\frac{5}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{900}{ \color{blue}{45} }x+ \frac{108}{ \color{blue}{45} })& = & (\frac{-405}{ \color{blue}{45} }x+ \frac{25}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 900x \color{red}{+108} & = & \color{red}{-405x} +25 \\\Leftrightarrow & 900x \color{red}{+108} \color{blue}{-108} \color{blue}{+405x} & = & \color{red}{-405x} +25 \color{blue}{+405x} \color{blue}{-108} \\\Leftrightarrow & 900x+405x& = & 25-108 \\\Leftrightarrow & \color{red}{1305} x& = & -83 \\\Leftrightarrow & x = \frac{-83}{1305} & & \\ & V = \left\{ \frac{-83}{1305} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x+\frac{3}{11})& = & 7x+\frac{9}{10} \\\Leftrightarrow & -30x+\frac{18}{11}& = & 7x+\frac{9}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{-3300}{ \color{blue}{110} }x+ \frac{180}{ \color{blue}{110} })& = & (\frac{770}{ \color{blue}{110} }x+ \frac{99}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & -3300x \color{red}{+180} & = & \color{red}{770x} +99 \\\Leftrightarrow & -3300x \color{red}{+180} \color{blue}{-180} \color{blue}{-770x} & = & \color{red}{770x} +99 \color{blue}{-770x} \color{blue}{-180} \\\Leftrightarrow & -3300x-770x& = & 99-180 \\\Leftrightarrow & \color{red}{-4070} x& = & -81 \\\Leftrightarrow & x = \frac{-81}{-4070} & & \\\Leftrightarrow & x = \frac{81}{4070} & & \\ & V = \left\{ \frac{81}{4070} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x-\frac{2}{7})& = & 4x+\frac{7}{5} \\\Leftrightarrow & -15x+\frac{6}{7}& = & 4x+\frac{7}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-525}{ \color{blue}{35} }x+ \frac{30}{ \color{blue}{35} })& = & (\frac{140}{ \color{blue}{35} }x+ \frac{49}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -525x \color{red}{+30} & = & \color{red}{140x} +49 \\\Leftrightarrow & -525x \color{red}{+30} \color{blue}{-30} \color{blue}{-140x} & = & \color{red}{140x} +49 \color{blue}{-140x} \color{blue}{-30} \\\Leftrightarrow & -525x-140x& = & 49-30 \\\Leftrightarrow & \color{red}{-665} x& = & 19 \\\Leftrightarrow & x = \frac{19}{-665} & & \\\Leftrightarrow & x = \frac{-1}{35} & & \\ & V = \left\{ \frac{-1}{35} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x+\frac{5}{8})& = & -7x+\frac{4}{3} \\\Leftrightarrow & 9x-\frac{15}{8}& = & -7x+\frac{4}{3} \\ & & & \text{kgv van noemers 8 en 3 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{216}{ \color{blue}{24} }x- \frac{45}{ \color{blue}{24} })& = & (\frac{-168}{ \color{blue}{24} }x+ \frac{32}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 216x \color{red}{-45} & = & \color{red}{-168x} +32 \\\Leftrightarrow & 216x \color{red}{-45} \color{blue}{+45} \color{blue}{+168x} & = & \color{red}{-168x} +32 \color{blue}{+168x} \color{blue}{+45} \\\Leftrightarrow & 216x+168x& = & 32+45 \\\Leftrightarrow & \color{red}{384} x& = & 77 \\\Leftrightarrow & x = \frac{77}{384} & & \\ & V = \left\{ \frac{77}{384} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x+\frac{3}{7})& = & -7x+\frac{3}{4} \\\Leftrightarrow & -10x-\frac{6}{7}& = & -7x+\frac{3}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-280}{ \color{blue}{28} }x- \frac{24}{ \color{blue}{28} })& = & (\frac{-196}{ \color{blue}{28} }x+ \frac{21}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -280x \color{red}{-24} & = & \color{red}{-196x} +21 \\\Leftrightarrow & -280x \color{red}{-24} \color{blue}{+24} \color{blue}{+196x} & = & \color{red}{-196x} +21 \color{blue}{+196x} \color{blue}{+24} \\\Leftrightarrow & -280x+196x& = & 21+24 \\\Leftrightarrow & \color{red}{-84} x& = & 45 \\\Leftrightarrow & x = \frac{45}{-84} & & \\\Leftrightarrow & x = \frac{-15}{28} & & \\ & V = \left\{ \frac{-15}{28} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x-\frac{4}{3})& = & 5x+\frac{5}{2} \\\Leftrightarrow & -4x+\frac{8}{3}& = & 5x+\frac{5}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-24}{ \color{blue}{6} }x+ \frac{16}{ \color{blue}{6} })& = & (\frac{30}{ \color{blue}{6} }x+ \frac{15}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -24x \color{red}{+16} & = & \color{red}{30x} +15 \\\Leftrightarrow & -24x \color{red}{+16} \color{blue}{-16} \color{blue}{-30x} & = & \color{red}{30x} +15 \color{blue}{-30x} \color{blue}{-16} \\\Leftrightarrow & -24x-30x& = & 15-16 \\\Leftrightarrow & \color{red}{-54} x& = & -1 \\\Leftrightarrow & x = \frac{-1}{-54} & & \\\Leftrightarrow & x = \frac{1}{54} & & \\ & V = \left\{ \frac{1}{54} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x-\frac{3}{5})& = & 5x+\frac{2}{11} \\\Leftrightarrow & -9x-\frac{9}{5}& = & 5x+\frac{2}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-495}{ \color{blue}{55} }x- \frac{99}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{10}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -495x \color{red}{-99} & = & \color{red}{275x} +10 \\\Leftrightarrow & -495x \color{red}{-99} \color{blue}{+99} \color{blue}{-275x} & = & \color{red}{275x} +10 \color{blue}{-275x} \color{blue}{+99} \\\Leftrightarrow & -495x-275x& = & 10+99 \\\Leftrightarrow & \color{red}{-770} x& = & 109 \\\Leftrightarrow & x = \frac{109}{-770} & & \\\Leftrightarrow & x = \frac{-109}{770} & & \\ & V = \left\{ \frac{-109}{770} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x+\frac{5}{3})& = & -7x+\frac{9}{2} \\\Leftrightarrow & -16x+\frac{20}{3}& = & -7x+\frac{9}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-96}{ \color{blue}{6} }x+ \frac{40}{ \color{blue}{6} })& = & (\frac{-42}{ \color{blue}{6} }x+ \frac{27}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -96x \color{red}{+40} & = & \color{red}{-42x} +27 \\\Leftrightarrow & -96x \color{red}{+40} \color{blue}{-40} \color{blue}{+42x} & = & \color{red}{-42x} +27 \color{blue}{+42x} \color{blue}{-40} \\\Leftrightarrow & -96x+42x& = & 27-40 \\\Leftrightarrow & \color{red}{-54} x& = & -13 \\\Leftrightarrow & x = \frac{-13}{-54} & & \\\Leftrightarrow & x = \frac{13}{54} & & \\ & V = \left\{ \frac{13}{54} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x+\frac{5}{7})& = & -7x+\frac{8}{11} \\\Leftrightarrow & -30x-\frac{30}{7}& = & -7x+\frac{8}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-2310}{ \color{blue}{77} }x- \frac{330}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{56}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -2310x \color{red}{-330} & = & \color{red}{-539x} +56 \\\Leftrightarrow & -2310x \color{red}{-330} \color{blue}{+330} \color{blue}{+539x} & = & \color{red}{-539x} +56 \color{blue}{+539x} \color{blue}{+330} \\\Leftrightarrow & -2310x+539x& = & 56+330 \\\Leftrightarrow & \color{red}{-1771} x& = & 386 \\\Leftrightarrow & x = \frac{386}{-1771} & & \\\Leftrightarrow & x = \frac{-386}{1771} & & \\ & V = \left\{ \frac{-386}{1771} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x+\frac{2}{5})& = & -5x+\frac{3}{7} \\\Leftrightarrow & 24x+\frac{12}{5}& = & -5x+\frac{3}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{840}{ \color{blue}{35} }x+ \frac{84}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{15}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 840x \color{red}{+84} & = & \color{red}{-175x} +15 \\\Leftrightarrow & 840x \color{red}{+84} \color{blue}{-84} \color{blue}{+175x} & = & \color{red}{-175x} +15 \color{blue}{+175x} \color{blue}{-84} \\\Leftrightarrow & 840x+175x& = & 15-84 \\\Leftrightarrow & \color{red}{1015} x& = & -69 \\\Leftrightarrow & x = \frac{-69}{1015} & & \\ & V = \left\{ \frac{-69}{1015} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x+\frac{4}{9})& = & -7x+\frac{7}{8} \\\Leftrightarrow & -16x+\frac{16}{9}& = & -7x+\frac{7}{8} \\ & & & \text{kgv van noemers 9 en 8 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{-1152}{ \color{blue}{72} }x+ \frac{128}{ \color{blue}{72} })& = & (\frac{-504}{ \color{blue}{72} }x+ \frac{63}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & -1152x \color{red}{+128} & = & \color{red}{-504x} +63 \\\Leftrightarrow & -1152x \color{red}{+128} \color{blue}{-128} \color{blue}{+504x} & = & \color{red}{-504x} +63 \color{blue}{+504x} \color{blue}{-128} \\\Leftrightarrow & -1152x+504x& = & 63-128 \\\Leftrightarrow & \color{red}{-648} x& = & -65 \\\Leftrightarrow & x = \frac{-65}{-648} & & \\\Leftrightarrow & x = \frac{65}{648} & & \\ & V = \left\{ \frac{65}{648} \right\} & \\\end{align}\)