Hello and welcome to our lesson about variable expressions. Today we're going to look at different sample questions. The first question is that we're going to substitute and solved for these equations we're going to solve is x equal to 1 >Solve for x = 1 x + 2 = X + 3= X + 4= So what that means is that each of these questions were just going to duly called substitution.we are going to substitute the 1 in for every place that we see x alright So in this case the question will that turn into and I know this seems like a really simple question I wanted to come to start off easy this question will turn into a x plus 2 it will turn into 1 plus 2 where which is substituting the 1 for x 1 plus 2 is equal to the 3 in my math class alright. >Solve for x = 1 x + 2 = 1 + 2 =3 X + 3= X + 4= Alright, good so far, that's when we do the same thing we substituted one for action it becomes 1 plus3 which is equal to 4 >Solve for x = 1 x + 2 = 1 + 2 =3 X + 3= 1 + 3=4 X + 4= For final one we will that change that the 1 plus 4 which is equal to 5 >Solve for x = 1 x + 2 = 1 + 2 =3 X + 3= 1 + 3=4 X + 4= 1+4=5 This is the way that we are going to be doing these as every time you say x is equal to 1 essentially all we're going to be doing is plugging in value of 1 everywhere you see X okay let's look at some questions are a little bit more challenging. >Solve for x =2 4x = 3x + 1= 2x + 1 -x= Here's the first type of question when you have a number right next to the variable x okay when you substituted in a value of 2 right in there it is implied that you are actually multiply those two numbers alright so this is like you think 4 times 2 and it can be written with the parentheses >4x = 4(2) Okay 4 times 2 or it could be written for with a dot in between for the 4 and the 2 But either way we're substituting the value x equal in 2 just the same as we did in the last just plugged it to right into the equation 4 times 2 is equal to 8 >Solve for x =2 4x = 4(2) =8 3x + 1= 2x + 1 -x= Alright, so this next one still be 3 wheeler we're substituting in the value of 2 for X so 3 times 2 plus 1 >3x + 1= 3(2)+1= So get were were making ourselves have a little bit longer, have a question here the 3 times 2 is 6 plus 1 is equal to 7 >Solve for x =2 4x = 4(2) =8 3x + 1= 3(2)+1=7 2x + 1 -x= And we do have to do order of operations Here 3(2) so this is multiplication first and the addition second so is the order that we're doing it, in this case we have Two x here in side of the equation so are what are questions going to look like in the next line is 2 times and we substituted the value 2 in for x plus 1 minus and we're going to substitute in the value of 2 for x ok. >2x + 1 -x= 2(2) + 1 -2= We plug the 2 in every place we see x so 2 times x plus 1 minus 2 alright and we going to use the order of operations with the multiplication first 2 times 2 is equal to 4 everything else remain the same >2x + 1 -x= 2(2) + 1 -2= 4+1-2= So we'll have 4 plus 1 minus 2 and now because we have just addition and subtraction we can complete this question 4 plus 1 is 5 minus 2 is equal to Three >Solve for x =2 4x = 4(2) =8 3x + 1= 3(2)+1=7 2x + 1 -x= 2(2) + 1 -2= 4+1-2=3 Again, our questions are going to become a little bit more complicated Here >Solve when x = 2 and y = 3 x + y - 2 = 2x + 4y - 5 = We're going to have an X and a Y alright so x is equal to 2 y is equal to 3 we're just gonna plug in the numbers just like we did before. so where you see x you put in 2 Where you we see y you put in the 3 alright so what we have is 2 plus 3 minus 2 alright 2 plus 3 is 5 minus 2 is was equal to 3 So there's a final answer for that Question >Solve when x = 2 and y = 3 x + y - 2 = 2 + 3 - 2 = 3 2x + 4y - 5 = We're going to do this which is kinda the most complicated thing will see here 2x + 4y - 5 = We're going to substitute 2 in for X alright such 2 times 2 and 4 times our value for Y which is three Alright >Solve when x = 2 and y = 3 x + y - 2 = 2 + 3 - 2 = 3 2x + 4y - 5 = 2(2) - 4(3) - 5 = So we substituted in 2 for x, y is 3 for y, 2 times 2 and 4 times 3 and we can do both for those at the same time here 2 times 2 is 4, 3 times 4 is 12 ok. = 4 + 12 - 5 Now I can have them all together 4 plus 12 is 16 minus 5 is equal to 11 ok. = 11 >Solve when x = 2 and y = 3 x + y - 2 = 2 + 3 - 2 = 3 2x + 4y - 5 = 2(2) - 4(3) - 5 = 4 + 12 - 5 = 11 Now for the last page of equations we will let X equal 4 Y equals 7 Let x = 4 and y = 7 https://3.bp.blogspot.com/-V7YF5ABK4QM/V8tYpUREfDI/AAAAAAAAEU0/AOvObQYpLMY97IrcxV3VYVj7HzLy27xMACLcB/s1600/1.png We're going to do this exact same thing where we're going to plug in the values but this is using fractions so 7 times and i change my value X for 4 all divided by 7 https://3.bp.blogspot.com/-UaTiIzH-VE0/V8ta0_P0NSI/AAAAAAAAEVA/WkHrtWOTekIuPqg5QDEykFLgkO-QX96EQCLcB/s1600/1.png So I can do my multiplication first say 28 divided by 7 which is equal to 4 https://3.bp.blogspot.com/-E9-lR658bN4/V8tbnp9BTzI/AAAAAAAAEVE/GZFP4fp2VsAOnjK7dTrlW_UbEvjt7RvmwCLcB/s1600/1.png Okay, you get a lot done substituted X equals 4 Y equals 7 right into the equation 7 times 4 is equal to 28, 28 divided by 7 or 28 over 7 is equal to 4 ok. Now for the other question I'm going to Do the same thing. 3 and I'm going to substitute in my X Value by 4, 3 times 4 plus 2 divided by 7 https://1.bp.blogspot.com/-M3IhxZkfiDA/V8tenXJwqoI/AAAAAAAAEVM/IDo01oBNiuUmtEuMbBEWi2Y_U2Cv_gHsACLcB/s1600/1.png The first going to do the top part And then I'm going to take care of the fraction afterwards. Alright, so 3 times 4 is 12, 12 plus 2 divided by 7 and 12 plus 2 is 14 divided by 7 or the fraction of 14 over 7 is the same 14 divided by 7 is 2 https://4.bp.blogspot.com/-NEGf6MGop14/V8thCPc7YrI/AAAAAAAAEVU/ALKFp6aO5qICXuCld-h2qE1PVg31O76WwCLcB/s1600/1.png So that is your mini lesson for Today i hope it's been helpful